Tagged Questions

Questions related to real and complex logarithms.

28 views

49 views

Proof of a logarithm identity

I would like to know how to prove the following log identity: $x^{\frac{\log(\log(x))}{\log(x)}} = \log(x)$
79 views

Define the following functions $\mathbb{C}\to\mathbb{C}:$ $$u(z)=\frac{\log \left(z+\frac{1}{2}\right)}{z}\quad \left[-\pi\leqslant\arg \left(z+\tfrac12\right)<\pi\right];\quad v(z)=\frac{\log z}{z}... 1answer 25 views During the 56th month or the 57th month? A car depreciates in value according to the model$$V=Ak^t$$where £V is the value of the car t months from when it was new. Its value when new was £12499 and 36 months later its value was £... 2answers 49 views Complex logarithms when computing real-valued integral My question arise when I try to calculate real-valued integral, specifically, I want to evaluate the integral $$\int_0^1 \frac{\ln \left(\frac{x^2}{2}-x+1\right)}{x} dx$$ ... 7answers 1k views What is “8 log 2”? [closed] When someone says "8 Log 2" what does this equate to in writing? Does it mean the following?$$ \log _{2} 8 $$And if so, what is the value of this? When I plug those numbers into this log ... 3answers 117 views How to solve 3(a+1)(b+1)=3^a \times 2^b? Hi I'm new to logarithms and not sure how to solve equations involving logarithms. I managed to find this equation to answer a problem solving question, however now I do not know how to solve the ... 2answers 32 views Graphing log with number in front of “log” When I have something like y = log_2(x) I know that I have to turn it into exponential form and get: 2^y = x. Next, I make a table for X,Y and choose about 5 values for y, typically -1, 0, 1, ... 0answers 33 views Order Size estimation of converging sum used for approximation of logarithm I know it can be shown that \log n=\sum_{i=1}^\infty \frac{(n-1)^i}{in^i} for \forall n\in\Re where n\ge1 For given natural m, I tried to find the order size of k = f(m,n) in order for the ... 0answers 22 views Proof this limit superior is finite. Let \{ w_n \} be a sequence of non-negative numbers and put M_n=\sum_{k=1}^n w_k^2 \xrightarrow{n\to\infty} \infty . Proof that$$\limsup_{n\to\infty} \dfrac{\ln \ln \sqrt{M_n \ln \ln M_n} }{\ln \...
Just a bit confused about how to evaluate the following $$\log_3 8\times \log_5 9\times \log_2 5$$ What I have done so far: I have used the change of base rule to change each log to base $3$, ...