# Tagged Questions

Questions related to real and complex logarithms.

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### how to proceed next in this logarithmic inequality?

the question is $\frac{1}{log_4 (x+1)/(x+2)}$<$\frac{1}{log_4 (x+3)}$ I did the first step for defining the arguments of both sides and got $x\in(-3,-2)\cup (-1,\infty)$ next I did reciprocal ...
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### finding out total digits in a large number

Is there any easy way to find out how many digits does the number $12^{400}$ have or such types of problems like how many digits the number $x^y$ have? ($x$ and $y$ are variables)
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### Calculate the value of $e$ from integral definition

Starting with the definition of $e$ as $$\int_1^e \frac{dx}{x} = 1,$$ how can I show that $e = 2.718\ldots$?
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### 2 Weird questions

Seems like I'm full of weird mathematical questions! Last time I made a question about imaginary numbers. This time I have 2 seemingly unrelated questions. But nevertheless it's always good (and fun)...
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### Logarithmic equation solution

If $\frac {\log a}{b-c}=\frac{\log b}{c-a}=\frac{\log c}{a-b}$, then what would be the value of $a^{b+c}.b^{c+a}.c^{a+b}$? I'm unable to proceed.
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### Proof of logarithm inequality without continuity

Showing that the logarithm function is continuous in its domain boiled down to proving $$\frac{x}{1+x}\le \ln(1+x)\le x \ \ \text{for all}\ x >-1.$$ There are quite a few proofs already online. ...
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### How to solve the inequality $\log_2(4^x-2(2^x)+17)>5$?

Find the number of positive integers not satisfying the inequality $$\log_2(4^x-2(2^x)+17)>5$$ My approach: let $2^x=t$ then inequality is rewritten in form $$\log_2(t^2-2t+17)>5$$ then I ...
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### Order of growth rate in increasing order

This question is related to maths, so I post here. Actually it's a computer science question and I am facing this type of question while learning Design and Analysis of Algorithms, but we all know ...
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### Find the values of $b$ for which the equation $2\log_{\frac{1}{25}}(bx+28)=-\log_5(12-4x-x^2)$ has only one solution

Find the values of 'b' for which the equation $$2\log_{\frac{1}{25}}(bx+28)=-\log_5(12-4x-x^2)$$ has only one solution. =$$-2/2\log_{5}(bx+28)=-\log_5(12-4x-x^2)$$ My try: After removing the ...
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### Is this a pure imaginary number?

I've met this formula and I need to demonstrate that it is purely imaginary (it has no real part). $\frac{1}{2}\log(-\exp(i2\pi q))$, //for a real "input" q. As I don't know much about maths, what I'...
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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 $\log()$ the value $e$... and note that so far ...
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