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1.
Definition of logarithm
$\log_ba=x \iff b^x=a$
Logarithm
2.
Log of 1
$\log_a 1=0$
Logarithm
3.
Log of same numbers
$\log_a a = 1$
Logarithm
4.
Product rule for logarithms
$\log_a {xy}=\log_a x + \log_a y$
Logarithm
5.
Quotient rule for logarithms
$\log_a \dfrac{x}{y} = \log_ax - \log_ay$
Logarithm
6.
Power rule for logarithms
$\log_ax^n=n\log_ax$
Logarithm
7.
Log of square root
$\log_a\sqrt[n]{x}=\dfrac{1}{n} \log_ax$
Logarithm
8.
Change of base
$\log_ba=\dfrac{\log_ax}{\log_ay}$
Logarithm
9.
Change of base
$\log_ax=\dfrac{1}{\log_xa}$
Logarithm
10.
$a^{\log_ax}=x$
Logarithm
11.
Base 10 logarithm
$\log_{10}x = \log x$
Logarithm
12.
Natural logarithm
$\log_e x = \ln x, e=2.718281...$
Logarithm
13.
Log to Ln
$\log x = \dfrac{\ln x}{\ln 10}$
Logarithm
14.
Ln to Log
$\ln x = \dfrac{\log x}{\log e}$
Logarithm
15.
$\lim{x \to 0} \left(\dfrac{a^x-1}{x}\right)=\ln a$
Limit
Logarithm
16.
$\lim{x \to 1} \left( \dfrac{\ln x}{x-1} \right)=1$
Limit
Logarithm
17.
$\lim{x \to 0} \dfrac{\ln(x+1)}{x}=1$
Limit
Logarithm
18.
$\lim{x \to 0^+}x\ln x = 0$
Limit
Logarithm
19.
$\lim{x \to \infty}\dfrac{\ln x}{x} =0$
Limit
Logarithm
20.
$ \int \ln x dx = x\ln x - x + C$
Indefinite Integral
Logarithm

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