# Tagged Questions

3answers
1k views

### What's wrong with my aproach to solving this equation with multiple logarithms?

A question I was faced with asked "For which $x$ is $\log_{10}(x)^{\log_{10}(\log_{10}(x))}= 10,000$?" My instincts tell me I can say $$\log_{10}(x)=10$$ and $$\log_{10}(\log_{10}(x))=4$$ However, ...
5answers
379 views

### Am I allowed to apply L'Hospital's Rule inside of the natural logarithm function?

I have the following limit: $$\lim_{x\rightarrow \infty} \ln\left(\frac{2x^2+1}{x^2+1}\right)$$ If I was finding the limit of only the terms inside the natural log function, I would have the ...
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1answer
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### Why does this equation work?

let $P(x) := \sum_{p \leq x} Log [p]$, then we have $P(2^{k+1}) = \sum_{i=0}^k ( P(2^{i+1}) - P(2^i)) < 2 \cdot Log[2] \cdot (1 + 2 + 4 +... + 2^k) \leq 4 \cdot Log[2] \cdot 2^k$. Why does ...
2answers
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### Maximum likelihood estimate - help with calculating logs!

I'm doing a practice question finding the maximum likelihood estimate, but I'm having a bit of trouble with the actual 'pure' maths bit of it (the differentiation) I don't understand how you go from ...
5answers
109 views

### solve the equation using logarithms (I think this is easy level)

Solve the equation for $x$ by using base 10 logarithms. $$16\cdot4^{2.5x}=9$$ EDIT: I made a typo (somehow... I was very far off!!) The correct equation is this: $$16\cdot4^{2.5x}=70$$ Can it be ...
3answers
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1answer
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### Conversion of bases with logarithms

The question says if $\log_6(2)$ is $a$ and $\log_5(3)$ is $b$, express $\log_5(2)$ in terms of $a$ and $b$. I have tried the change of base formula for $ab$ to no avail, can someone give me a hint ...
0answers
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### Complex exponentiation

So I've got this question that is a bit difficult to ask, since it uses a term in my language that I can't properly translate into English. For $z\in\mathbb{C}^*$ and $a\in\mathbb{C}$ it would be ...
2answers
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### Help finding value of x in logarithms?

How to find the value of x in: $$10=8.4\log(0.3x+1)$$ so far I got : $$10=\log(0.3x+1)^{8.4}$$ $$10^{10}=(0.3x+1)^{8.4}$$ What should I do next?
1answer
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### Derivative of $\operatorname{Log}(\operatorname{Log}(z^2))$

Please help me with this question: (i don't know how to start) Suppose that $f(z)$ = $\operatorname{Log}(\operatorname{Log}(z^2))$. Find $f'(z)$ where it exists, and determine the set of points at ...
1answer
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2answers
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### Changing base of a logarithm by taking a square root from base?

From my homework I found $$\log_9{x} = \log_3{\sqrt{x}}$$ and besides that an explanation that to this was done by taking a square root of the base. I fail to grasp this completely. Should I need to ...
2answers
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### Continuous compounding question

A population of rabbits starts out with $100$ rabbits. The growth rate is $11.7$% per day. Determine the exponential equation. Is it $$\mathbb {P(t)} = 100e^{11.7t}$$ Can you guys give me the ...
0answers
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### Mapping a deleting ray to a horizontal strip

So, this is my question: D is a domain obtained by deleting the ray $x\leq 0$. And $G(z)$ is a branch of $log(z)$ on $D$. I want to show that G maps D onto a horizontal strip of width $2\pi$. Show ...
1answer
176 views

### Logarithmic inequalities

Full disclosure: This is a homework problem, but my question is regarding a concept that came about during solving the problem, not the actual solution to the problem. Problem: Rewrite as geometric ...
2answers
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1answer
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### Asset Depreciation - Logarithms

How many years would it take for the value of a car purchased at 30 000 to fall to 15 000 if it depreciates by 15% in the first year and 12% every year after that? This is not actually graded ...