Base b logarithm

#[The base $b$ logarithm of $x$, $\log_bx$, is the exponent to which you need to raise $b$ in order to obtain $x$. In symbols,][El logaritmo de $x$ en base $b$, $\log_bx$, es el exponente a la cual hay que elevar $b$ para obtener $x$. Simbólicamente,]# #[Note][Nota]#
1. $\log_b x$ is only defined if $b$ #[and][y]# $x$ are both positive, and $b \neq 1$.
2. $\log_{10} x$ is called the common logarithm of $x$ and is sometimes written as $\log x$

#[Examples][Ejemplos]#

The following table lists some exponential equations and their equivalent logarithmic form.

Exponential form	Logarithm form
$4^2=16$	$\log_416=2$
$2^3=8$	$\log_28=3$
$10^3=1{,}000$	$\log_{10}1{,}000=3\ $ #[or][o]# $\ \log 1{,}000 = 3$
$5^1=5$	$\log_55=1$
$7^0=1$	$\log_71=0$
$4^{-2}=\dfrac{1}{16}$	$\log_4\left(\dfrac{1}{16}\right)=-2$
$10^{-1}=\dfrac{1}{10}$	$\log_{10}\left(\dfrac{1}{10}\right)=-1\ $ #[or][o]# $\ \log\left(\dfrac{1}{10}\right)=-1$
$25^{1/2}=5$	$\log_{25}5=\dfrac{1}{2}$