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Laws of Indices and Logarithms

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Mathematics Teaching for Learning
Engineering Maths B, Exponents
August 18th, 2008 by Craig Rose
Permalink: http://www.craigsmaths.com/ea003-engineering-mathematics-b/laws-of-indices/

Engineering Maths B, Exponents
August 18th, 2008 by Craig Rose
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Memorise these indices and logarithms laws. Indices and logarithms are two different ways of saying the same thing. For example:

$y=\log_{a}x$ is read as “ $a$ raised to the power of $y$ equals $x$ “.

that is:

$a^{y}=x$ .

Hint: To check that you have remembered them correctly just substitute values for $a$ , $b$ , $m$ and $n$ .

$b = a^{n}$	$n = \log _a \left( b \right)$
$a^{m}\times a^{n}=a^{m+n}$	$\log _a \left( {mn} \right) = \log _a m + \log _a n$
$\frac{a^{m}}{a^{n}}=a^{m-n}$	$\log _a \left( {\frac{m}{n}} \right) = \log _a m - \log _a n$
$a^{m^{n}}=a^{mn}$	$\log _a \left( {m^n } \right) = n\log _a \left( m \right)$
$a^{0}=1$	$\log_{a}1=0$
$a^{m}\times b^{m}=\left(ab\right)^{m}$
$\frac{a^{m}}{b^{m}}=\left(\frac{a}{b}\right)^{m}$
$a^{-m}=\frac{1}{a^{m}}$
$a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$