# Tagged Questions

Questions related to real and complex logarithms.

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### How much proof is needed in such paper (Maths related)?

I'm writing a paper (report) regarding Euler's Number $\space e \space$ (even though he didn't discover it). Within this paper, I show that: $${d\over dx} {e^x} = {e^x}$$ **NOTE: ** This is not ...
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### Logarithm in the exponent

$$(2x)^{\log 2} = (3y)^{\log 3} \\ 3^{\log x} = 2^{\log y}$$ Solve for $x$ and $y$. My intuition for solving such problems is taking the logarithm on both sides but it does not work. I also ...
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### What is the value of $x$ in this logarithmic inequality? [closed]

Please help me with this inequality : $$\log_2 (x^2-2x) - 3 >0$$
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### If the integral of $c/x$ is $c.log(x)+C$ what is the base?

This question is a follow up to an answer I gave here: How to integrate $1/x$? After the algebra I said that 'This step of course gives the argument of $ln()$ the value $e$ and note that so far we ...
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### Calculating the amount of times a binary search could run (worse case) without a calculator/calculating base 2 logs without a calculator.

Ok so I had a question on a test that I had to do without a calculator. And I can not figure out how in the world I am supposed to do it without a calculator. The question asked to find how many ...
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### Logarithm question with base change

If $\log_{12} 27 = a$ then find the value of $\log_6 16$.
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### Can someone please explain how $60+\ln(64)-\ln(8)$ is equal to $60+\ln(8)$ [closed]

Can someone please explain how $60+ \ln(64)- \ln(8)$ is equal to $60+\ln(8)$. I can't understand why this is true.
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### what is the value of $x$ in this logarithmic question? [closed]

What is the value of $x$: $$x^{\log_5 x} >5$$ Thanks for the help.
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### Is $n^\frac{1}{10} \in O((\log n)^{10})$?

This question came up in a recent discussion: is $n^\frac{1}{10} \in O((\log n)^{10})$? First time I've come across a power of a log in a long time, and as far as I recall, there are no identities ...
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### A fast converging limit for $\ln x$ (or why $\ln 2 \approx \sqrt{\sqrt{42}-6})$

I've read a lot about approximating logarithms recently, and apparently it's not easy. It can be done by Taylor series (slow convergence), by continued fractions (also slow) and also by some limits. ...
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### I need to integrate $\ln(x^2)$ but I can't seem to get it right.

I have an issue that requires me to integrate $\ln(x^2)$ and I know it's done through integration by parts, but I just can't seem to get it right. Does anyone know how it would work out?
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### Generator Powers

I have factor base such that $$B=\{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47\}$$ I need to construct a program which inputs a prime "p" (p>72) and an integer "a", then outputs the 15 distinct values ...
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### Newtons Law Of Cooling (And Heating)

Rule is: $D= A.e^{-kt}$, Where: $k,a$ are elements of real numbers, $D$ is the difference between the temperature of the item and the surrounding air, and t is the time in hours since the object ...
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### $\log_{10}y = m\log_{10} x + \log_{10} c$ for straight line

Express $x$ in terms of $y$: $\log_{10}y = 2\log_{10}x + \log_{10} c$ When $x = 0$ $$2 = \log_{10} c$$ $$c = 100$$ $$\log_{10} y = 2\log_{10}x + \log_{10} c$$ $$\log_{10}y = \log_{10}(x^2c)$$ ...
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### Solve $\log_9(x-4) - \log_9(x-8)= \frac{1}2$

Solve $\log_9(x-4) - \log_9(x-8)= \frac{1}2$ $(x-4) - (x-8)= 9^\frac{1}2$ $(x-4) - (x-8)= 3$ The answer is 10 but I am not sure how that was obtained.
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### How to solve $ax + b \log x =c$ or $\frac{a}{x}+b\log x=c$?

Here $a,b,c$ are any real numbers. We can use graphical methods using Mathematical tools, but what are the other techniques ?
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### write $\log_42x$ in the form $y =\log_4x+k$

write $\log_42x$ in the form $y = \log_4x+k$ I take it this is one of the log rules but I don't see which and I do not understand where k comes from or what the constant stands for.
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### Find the value of 'x'

What is the value of x, if: $$(\log_{10} 4 )^2 + (\log_{10} 4 )^4+ (\log_{10} 4 )^{16}+ (\log_{10} 4 )^x = 6?$$
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### Estimating elasticity of y with respect to x in a log-log specification

The question My rudimentary workings so far is that; log(y_i/x_i) = log(y_i)-log(x_i) Factorise, so, log(y_i/x_i) = log(y_i) + upsilon_i - log(gamma_i + 1) Thus, elasticity of y to x is always >1 ...
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### How can I rearrange this logarithmic formula to be computer friendly?

I've had a look through the logarithmic identities on Wikipedia, but nothing fits the bill. Basically, I have a formula which shows how much more 'risky' one number is compared to another, where 0 = ...
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### Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$

I was given a task to prove that inequality is true for x>0: $(e^x-1)\ln(1+x) > x^2$. I've tried to use derivatives to show that the $f(x) = (e^x-1)\ln(1+x)-x^2$ is greater than zero, but has never ...