I'm quite new to this topic and I'm curious if the question above is possible. Based on what I searched in the internet, you can't take the logarithm of a number with a negative base; and, the logarithm of a negative number is undefined. Does this mean that we can't take the logarithm of a negative number with a negative base?
Example is log(-64) with base (-4) = x. So if we transform it into a exponential equation and solve it further then it should be
(-4)^x = -64
(-4)^x = (-4)^3. Applying common base property of equality
Then log(-64) with base (-4) = 3
So it should be possible right?
Edit: thanks to all who replied! Y’all have really helped me with my math class- I don’t know how I got to precalc in college not understanding what these are, but I definitely get it much more than I did before. I’m too lazy to go to each response and thank y’all, so this is what I’m doing instead :)
Hi my friend just replaced h with h/2 on the left side and thus showed that this inequality is true. I am a little confused, am I really just allowed to do that? Dividing the left side with 2 would give me a different result right? I am really not familiar with logarithms.
This is the question at hand :
If the equation log(ax)*log(bx)+1=0, with a > 0, b > 0, has a solution x > 0, it follows that b/a >= _____ or ____>=b/a>____
I partly arrived at the answer, this is my work :
since Log(ax)*Log(bx) = -1
we can assume one must equal +1 and the other must be -1, so:
log(ax)=1 ==> ax=10 ==> a=10/x
log(bx)=-1 ==> bx=1/10 ==> b=1/(10x)
now I will multiply b by 10 to get 10b=10/(10x), since a=(10/x), this can be written as :
divide both by 10 to get b=a/100, thus, b/a=1/100.
this is partly correct, the real answer is that b/a>=100 OR
I honestly don't understand where the inequality is coming from and why b/a can be over 100.
ps: sorry for the poor formatting
Knowing the theory is insufficient in scoring highly in Section 3 of the GAMSAT. One of the primary contributing factors in scoring 90, was the ability to contextualize skills and information to other applications. So what does that mean?
Firstly, it is important to understand the intuitive logic behind each of the concepts - if you cannot explain it simply, then you do not know it well enough. This ensures that you have an adequate grasp of the concept at hand. To make your life easier, I have listed some questions under key concepts as a prompt - for instance, when is the pH equal to the pKa and why?
The next step is to then identify common areas of application of this concept, so that you can grasp how it works in action. In the case of Arrhenius acids, one common area would be in titration, where exists an abundance of quantitative or graphical questions that can be thrown at you.
Lastly, it is a good idea to identify key skills that you are not sufficient in, for instance interpreting logarithms. This is such a common skill tested in the GAMSAT, yet many of us do not intentionally take the time to refresh it before the exam - it is akin to tossing away free marks.
Below includes a question for you to discuss, and dwell on. I have attached links to helpful websites to reduce the friction in your research. Make sure to keep a study journal of the things that trip you up, or anything you wish to revisit - spaced repetition is proven to work. Best of luck.
This is part of a four-times a week free GAMSAT Digest. PM for more!
🧪 Topic – Arrhenius Acids
Arrhenius acids involve substances that dissociate in aqueous solutions to form hydrogen ions. Many common reactions involve water, making Arrhenius acid theory still relevant despite the existence of the more advanced Bronsted-Lowry or Lewis acid theory.
This topic is commonly tested in GAMSAT due to the plethora of applications that involve skills suc... keep reading on reddit ➡
I'm having a hard time vocalizing with the correct math terms what seems common in engineering.
The goal is to figure out cost, but do estimates on the same 'scale(?)'. This is rounding to a log base 10 or 100? Or rather, by exponentials 10?
For instance, say we have a component that costs 167. I would round it to 100 or 200, it doesnt really matter because its Not 1000. Its also not 0. Its in the range of ~100.
Basically this is been a common communication problem for me because I don't know what word/phrasing I'm looking for. I feel like 'scale' isn't as accurate as using words like log or exponential. Can someone send me an example sentence on how I can communicate what is happening when I assume 167 is ~100 (or even ~200).
Is it possible that 5 log5-2 log5=3 log5
Is there any other way to solve 3^(2x+1) - 2(3^(x+½)) - 3 = 0 other than replacing 3^x with an unknown?
Thank you :)
I'm currently having to do some logarithms as homework. I understand most of them, but this one is completely stumping me. The question is to write down the following equation as one logarithm:
3 ∙ ^(4)log(x) + 2 ∙ ^(8)log(x+1)
The answer, according to the book I'm using is: ^(4)log(x^(3) * (x+1)^(4/3))
I understand how they achieve the x^(3) but I've no idea where the ^(4/3) exponent comes from or how they get from ^(8)log to ^(4)log.
I've tried making the bases equal:
log(x)^(3) / log 4 + log(x+1)^(2) / log 8
then I've tried to equalize the logs underneath:
log(x)^(3) / log 2^(2) + log(x+1)^(2) / log 2^(3)
log(x)^(3) / 2 ∙ log 2 + log(x+1)^(2) / 3 ∙ log 2
But from this point I don't really know what to do
Help would be greatly appreciated. Thanks in advance.
hi, this is my first post. I need help with the logarithm recursion problem. any example or help will be useful to me.
need to resolve the logarithm recursion for the following examples.
tn - 2tn-1 = 2n
tn - 2tn-1 = n3n
tn - tn-1 = n
Hello could someone please help me with the following and show there working out.
Log4 X = -2 1/2
Log8 X = -4/3
Many thanks - first time tackling logarithms today!
Meanwhile, log[z^(1/N)] = (1/N)log(z). I have been reading that it has something to do with set equivalence but I cannot understand this question. It seems paradoxical.
Thanks here is the problem.
Thank you to those who helped walk through me the problem!! I guess I was focusing so much on the wrong areas when the answer was literally right in front of me...
How do you find.
Log-5 (8y-6) - Log-5 (y-5)=log-4 (16)
Note "-" means base. Answer 31
Suppose I have a variable "X". Suppose "X" has many values that are 0 and many large values.
E.g. X: (0,0,0,0,56677, 876433, 8765432, 0,0,99999)
For instance, I want to take the log(X) so it's easier to plot X on a graph and visualize it.
Of course, we can not take the log(0).
My question: Is it a valid approach to replace 0 with a small number (e.g. 1)
X: (1,1,1,1,56677, 876433, 8765432, 1,1,99999)
Now you would be able to take the log(X)
Suppose I had two variables (X, Y).
If I did this "transform" of X and then took the log(X) ... could I plot log(X) vs Y?
If you had no table of logarithms, and weren't about to make one, what's a good way to calculate decimal exponents on a soroban? There's 11 things that you could memorize - or write down - that would help. First, memorize that e^0.693 approximates 2. Second, have a table handy of only ten items - the values of e raised to 0.1 through 0.9. Or you could memorize it. It's not necessary to have more than this.
Perhaps civilization has fallen and you are on a sandy beach with your soroban. You have drawn Pascal's Triangle in the sand, and remember that 1.1^10 is an approximation of e. You remember that 1.01^100 is a better approximation. And so on. Maybe you settle for 1.001^1000. The point is that, by using a soroban and Pascal's Triangle, it's not terribly hard to come up with a table of values of e. Tedious, but not difficult, using the powers of 1.001. You can get your approximation of the values of e to 0.1, 0.2, 0.3 and up to 0.9. But having it written down (or memorized) would be better. perhaps on a laminated card or on a bracelet?
So, someone asks - perhaps the engineer stranded with you on the island - what's 2 raised to the power of 1.3? Using 1.3 times 0.693, you get approximately 0.9. The question is like asking what's e to the power of 0.9. And you know that answer.
But let's assume a harder question, like 5^6.7, while the cannibal zombies are chasing you both down the beach. I know it might be difficult to keep the soroban level and not bouncy during such an exercise, but let's assume that the cannibal zombies are the slow type. Finding the log of 5 base 2, and moving every so often to hide from the zombies, you get a multiplier of 2.32 (more or less). so 5^6.7 is really 2^15.54. Well, now my example has broken down, because not only is it fairly easy to find 2^15 on a soroban, but the square root of 2 is something that you'd typically memorize. So, let's scramble for a new example number, like - oh - 2^3.7 ... there's that's an odd-looking number, indeed.
But back to the zombies. You have clambered, hooves and all, to the top of a roof and the zombies are clustering around the base. The neigh-gineer needs you to calculate 2^3.7 in a hurry. So, he's basically asking what's 8 times 2^0.7? Hurriedly, you calculate that 0.7 times 0.693 is 0.4851. It's tough to slide those beads under pressure, but you manage. That's roughly 0.5, and you have a table with e^0.5 on it. Multiplying 8 times 1.65, you get 13.2 (instead of 13... keep reading on reddit ➡
Express y in terms of x.
3 + log2 (x + y) = log2 (x - 2y)
Step 1: Convert 3 to log2^? = 3, 2^3 = 8
Step 2: log2^8 + log2 (x + y ) = log2 (x - 2y)
Step 3: log2 ( (8) (x + y) ) = log2 (x - 2y)
Step 4: (8) (x + y) = (x - 2y)
Step 5: (8x + 8y) = (x - 2y)
Step 6: 8x = x - 10y
Step 7: 7x = -10y
Step 8: x = (-10y / 7)
Step 9: Repeat step 5 to step 8 to find "y"?
Step 10: y: -7x/10
As the titel says I need help with labels on Histograms. I'm displaying a logarithmic version of earnings-variables, as to have a bell-curved shape. But I want to display the exponential versions of the values on the X-axis. I've been trying to change this in the graph editor but it messes up the chart.
Thanks in advance
I’m trying to help a friend with a problem. I know logarithms, but she doesn’t. We are trying to solve for t.
Does anyone know of a way to solve this without using logarithms?
For example: log3
if it doesn't have a base, how is this useful?
What is it referring to? why is it there? How was this originally deduced? why does it make sense?
I am missing something, can someone please explain?
If a function f(x) satisfies f=uv for some differentiable functions u(x) and v(x), then
log f = log u + log v
⇒ f'/f = u'/u + v'/v
⇒ f' = f * (u'/u + v'/v) = uv * (u'/u + v'/v) = u'v + v'u.
Tadaa! Much easier than doing the whole f(x+h) thing.
In chapter 5 - The diagonal alley, from the book Harry Potter and the philosopher's stone, Harry is taken to vault 687 of Gringotts, the bank of wizards, on his 11th birthday and discovers that he has a small fortune. Consider that on that day the fortune found by Harry corresponded to 50,625 galleons and that the annual income in Gringotts was, on average, 5% per year.
a) How long does it take for the value of the fortune to equal 205,942.50 galleons?
Use: log2 = 0,301, log3 = 0,477, log7 = 0,845 and log113 = 2,053
b) Knowing that Harry Potter was born on July 31, 1980, on what day, month and year did the fortune reach the amount above?
I know there are some months that have 28 and 31 days, so i think maybe my A is wrong too(171,85 years), it can`t be that many years to count. Please help!
This is a paragraph from my calculus textbook (Stewart). I don't understand why the formula it uses for the power rule of logarithms requires r to be rational. Doesn't this rule also work for irrational values of r? A bit later, the book defines e^x, which might relate to the reason for the way it introduced the power rule, but I'm not sure. To be honest, I also don't really understand why the book "defines" e^x for irrational numbers when it had just acted like the formula only worked for rationals - it seems to be out of nowhere, of no logical consequence. I'd greatly appreciate if anyone could help me understand all the connections and reasons I might not be seeing here. Thanks.
https://imgur.com/a/Hkbc5he self taught so I only know the basics and got completely stuck on this.
How can I re-write the two terms:
log2(2^(a)) = 2^(a/2)
Given that a here is an expression such as x+1?
Given that log2 k=a and log3 k=b, find logk 12 in terms of a and b.
The answer supposed to be 2b+a ÷ ab
I don't know how to simplify the logk 12 into that answer
so im having a strange problem with my new CXII, when i input log(370) it just outputs the same thing. i know this isnt a complex number, even google can output the answer, so would anyone happen to know why its not outputing the answer?
Edit: to be clear, it outputs log(370) instead of 2.whatever like it should. I’ve looked in the settings and nothing fixed it. Any help would be great :)
I personally pronounce it /lɒn/
I mean, if we are considering the average division time and that the event results in 2 bacteria, why is a natural logarithm used to describe the population across time?
Just read about graph algorithms and learned how the logarithm makes it possible to find the most probable route using the shortest path algorithm, which is usually used to find the closest distance!
>Now suppose you want to find the decay chain with the highest probability. You could do it by assigning each edge a “length” of -log λ and using a shortest path algorithm. Why? Because the shortest path algorithm adds up the lengths of the edges, and adding up log probabilities is the same as multiplying probabilities. Also, because the logarithms are negated, the smallest sum corresponds to the largest probability. So the shortest path corresponds to the most likely decay chain.
Hey guys... struggling again. Only a two days to go and I am making some progress (slowly) as I work through these practice questions. I am having trouble learning some of the basics regarding exponents and logarithms.
As you can see here: https://imgur.com/Cd9Rv5H
I am just not getting it. How can I determine these values: f(g(x)) and g(f(x)) ?
Also, how can I determine for which bases a is the logarithmic function, a decreasing one? Please see here: https://imgur.com/Sbdptye
^ Also worth mentioning - I know I got the answer correct, but I dont quite fully understand why (1,0) is the point that the graph passes. Please could someone explain?
The question to me is very confusing. I am not sure what form I am supposed to give the answer in either. Would really appreciate an explanation and some advice. Thanks so much in advance. I really owe you guys so much
In this article it says log 2 to the base 8 is 64. But how? Isn’t it 1/3 ?
In simple terms , exponent of a number is the logarithm of it answer if i am correct. I.e if a^b = c , b is logarithm of c to base a.
That way log 8 to the base 2, comes out as 3. Because 2^3 = 8. But how does log 2 to base 8 come out as 64?
Its also been mentioned that Logarithms are inverse of exponents. Another example they gave was that :
log x = 100. (To base 10) So what is x? The answer was 2. 10^x = 100 So x = 2
Isn’t log 100 to base 10 = 2 ?
Am i missing something here?
Thanks to XKCD, I noticed this phenomenon yesterday and proceeded to measure the distance on a slide rule. Pi appears to be just a hair lower than the midway point between 1 and 10.
The biggest point toward this being a coincidence is that while pi is a special number, ten is just humanity’s current base for math, hence our use of it to create logarithms involving ten.
Hello I have a question in case anybody can answer it. What does it mean to evaluate a logarithm in exact form? See the specific problem I am facing is that prior to now, I've simply been solving logarithms by dividing log 10 of the argument by the log 10 of the base. I am now doing the culminative activity for my course, and I've been asked to solve logarithms in exact form. No this is literally not come up before now, and this is the course review LOL. Oh well. Now I figured out how this works in regards to problems like log3 1/27. Those aren't an issue. I assume the idea of "exact form" is that there aren't a bunch of annoying decimal places because fractions are being used. Then the problem "log 25 - log 5/2" Comes in, And this just comes way out of left field at least it seems to be. Now I am not asking anybody to solve this equation for me, I really, really not. I just cannot understand how Nice and clean fractions can be used here… am I missing something?
I'd very much appreciate any responses! I can't really find a good explanation for this through a simple Google search, otherwise I wouldn't be asking here LOL. Thanks so much!
edit: thnx a bunch for all of your responses! this was immensly helpful
(6^(2x+1) )/26 = 6^3
My teacher sent me a list of topics for precalc so I'll know what will be on the exam to test out of it, and this is one of the topics under exponents. I really don't know how to solve this.
It says logc(16) = a and logc(9) = b, evaluate the logs under, which would need to know the value of 'c' to do.
So I did c^a = 16 and c^b = 9. Except I can't think of any one number that can be raised to an exponent to equal 16 AND 9. Just c^a = 16 could be 2^4, 4^2, or 16^1 and c^b = 9 could be 3^2, but none of those solutions are shared by both, so that means there's solution that satisfies both a and b?
Like when talking about time complexity, if something is O(log(n)) then that means log base 2 of n, which isn't intuitive to someone who is just learning about time complexity. Fortunately out of all the different videos and reading I've done for CS in general, but more specifically for understanding time complexity, one video that I remember took the time to clarify, "Oh yeah, by the way, when talking about log in programming, it's almost always referring to base 2".
I feel like this should be a more commonly said bit of information.... why isn't it? Or is it and I just somehow haven't seen it much?
Hello I have been having problems with limits of functions that include logarithms. These limits aren't even of the type: lim(×->+infinity) so I can't solve them according to their order.
First limit: http://imgur.com/a/2lAA5d2
(Solution should be Log__4__(e) )
If you've ever been on here/read my posts, you may know I always post my attempt, but this limit...I don't even know where to start from? I tried multiplying both by 1/cos(x) to have a log (1/2) (fraction) but I just am unsure, I always get the indeterminate form 0/0 and little or nothing to do in terms of factorisation/substitution by another variable.
The solution should be zero, I get e^+infinity , and can't understand what I did wrong
Thank you in advance
I have tired to solve but i'm not sure if this is right
I can't seem to get the correct answer of "54.25 years", can someone explain what I can do to fix this? Thanks if you know