Logarithm

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A logarithm is a shorthand way of expressing exponentional notation.

Introductory

The general form for a logarithm can be expressed as $log_x y=z$ which means $x^z=y$. We would read this as "The logarithm of y base x is z". We have $3^3=27$. To express this in Logarithmic notation, we would write it as $log_3 27=3$. When a logarithm has no base, it is assumed to be base 10.

Logarithmic Properties

These hold for all logarithms.

  • $log_a b^n=nlog_a b$
  • $log_a b+ log_a c=log_a bc$
  • $log_a b-log_a c=log_a \frac{b}{c}$
  • $(log_a b)(log_c d)= (log_a d)(log_c b)$
  • $\frac{log_a b}{log_a c}=log_c b$
  • $log_a^n b^n=log_a b$
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