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What is a logarithm?

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Oct 15, 2014

The logarithm base $b$ $b$ of a number $n$ $n$ is the number $x$ $x$ that when $b$ $b$ is raised to $x$ $x$ th power, the resulting value is $n$ $n$

${log}_{b} n = x \Leftrightarrow b^{x} = n$ $log_b n = x <=> b^x = n$

Example:

${log}_{2} 8 = x$ $log_2 8 = x$

$\Rightarrow 2^{x} = 8$ $=> 2^x = 8$
$\Rightarrow 2^{x} = 2^{3}$ $=> 2^x = 2^3$
$\Rightarrow x = 3$ $=> x = 3$

${log}_{5} 1 = x$ $log_5 1 = x$
$\Rightarrow 5^{x} = 1$ $=> 5^x = 1$
$\Rightarrow 5^{x} = 5^{0}$ $=> 5^x = 5^0$
$\Rightarrow x = 0$ $=> x = 0$

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