Loading subject…
Change of base formula
For $a>0$, $a\neq 1$, $b>0$, and any convenient base $c>0$, $c\neq 1$:
$$\log_a b=\frac{\log_c b}{\log_c a}$$
Common choices are $c=10$ (using $\log$) or $c=e$ (using $\ln$).
Logarithm
For $a>0$, $a\neq 1$, and $x>0$, $\log_a x$ is the exponent $k$ such that $a^k=x$.
Power rule
$\log_a(x^n)=n\log_a x$ (for real $n$, as long as $x^n$ is defined and $x>0$).
Product rule
$\log_a(xy)=\log_a x+\log_a y$.
Quotient rule
$\log_a\left(\frac{x}{y}\right)=\log_a x-\log_a y$.