Why does $ 1 + \frac 13 . \frac 14 + \frac 15 . \frac 1{4^2} + \frac 17 . \frac 1{4^3} + ..... = \log 3 $?
13085
Evaluate $ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$
23128
Why aren't logarithms defined for negative $x$?
64800
Evaluate $\int_0^1 \log \left( \frac{x^2+\sqrt{3}x+1}{x^2-\sqrt{3}x+1} \right) \frac{dx}{x} $
148461
If $S=\frac{1}{1+1^2+1^4}+\frac{2}{1+2^2+2^4}+\cdots+\frac{n}{1+n^2+n^4}$, then calculate $14S$.
150991
What is the order of the sum of log x?
115992
Integrating $\frac{\log(1+x)}{1+x^2}$
37871
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
30835
Logarithm proof problem: $a^{\log_b c} = c^{\log_b a}$
133614
Why is $x^{\log_x n}=n$?
136185
How $a^{\log_b x} = x^{\log_b a}$?
144801
$1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\dots+\frac{1}{1331}=\frac{p}{q}$; is $p$ divisible by $1997$?
124248
$1+\frac {1}{4}(1+\frac {1}{4}) +\frac {1}{9}(1+\frac {1}{4} +\frac {1}{9})+....$
128953
Why $\frac{\log(x)}{\log(y)}$ gives the same value as $\frac{\ln(x)}{\ln(y)}$
133485
How to solve $\int_0^{\infty} \frac{\log(x+\frac{1}{x})}{1+x^2}dx$?
100037
nth roots and logarithm
100896
What is the sum of this? $ 1 + \frac12 + \frac13 + \frac14 + \frac16 + \frac18 + \frac19 + \frac1{12} +\cdots$
96039
Why is $\frac {1\cdot2\cdot3\cdot...\cdot n}{(n+1)(n+2)...(2n)}\le \frac 1 {n+1}$