# Tagged Questions

Questions related to real and complex logarithms.

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### How do I solve this tricky logarithmic formula

I have a formula as follows: $0.55508389365 = \ln(20 + x)/\ln(240 +x)$ I happen to know that x = 1 (approximately) is the solution. But I'm not sure how I would go about solving this if I didn'...
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### Prove that $\log(n!)\leq(\log(n))!$

Prove that $\log(n!)\leq(\log(n))!$ My attempt: I read somewhere that $n\leq\log(n!)\leq(\log(n))!$. But when I used calculator $\log(n!)$ can not be less than or equal to $(\log(n))!$. ...
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### How to solve $\log_2(x) +3 = \log_3(x+2)$ [on hold]

Hi Math Stack Exchange Communities, I am new here. I have a question regarding logarithm solving. Let's say I have this equation: $$\log_2 (x) +3 = \log_3 (x+2)$$ How can I solve this kind of ...
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### How to simplify the expression $(\log_9 2 + \log_9 4)\log_2 (3)$

Our test asked to simplify $(\log_9 2 + \log_9 4)\log_2 (3)$. I simplified the first parenthesis to be $\log_9 (8)$. So, now I have $\log_9 (8) \cdot \log_2 (3)$ and I can change to base $10$ and ...
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### how to get value of n if the value of n * log n is given? [duplicate]

Possible Duplicate: How can I solve for $n$ in the equation $n \log n = C$? how to get value of n if the value of n * log n is given ? I am stuck with this: ...
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### How to solve for log with a number outside?

$$\log_6(4x-10)+1 = \log_6(15x+15)$$ This is a sample problem. I know that when the bases of log are the same, all you have to do is set the parenthesis inside equal to each other. If the $1$ wasn't ...
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### Calculate $\log_{\frac{1}{2}}{(2\sqrt[3]{4})}$

I have this exercise:$$\log_{\frac{1}{2}}{(2\sqrt[3]{4})}$$ There is not equation or something else, how should I solve this type of exercise?
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### Steps to Graph Exponential Equations & Absolute Value

how to sketch: $-e^{|-x-1|} + 2$ Can someone clarify: $|f(x)|:$ we draw $f(x)$ and then reflect the ($-y$ parts) in the $x$-axis $f|(x)|:$ we draw $f(x)$ and then reflect the ($-x$ parts) in the $y$...
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### Basic Logarithms problems [duplicate]

Can someone tell me how many digits would be there in- $(2.5)^{200}$ and $6^{50}?$ I'm utterly confused where to begin from. Any help would be appreciable.