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# Logarithmic Functions

Logarithmic scales are used when the range of possible values is very wide, such as the intensity of an earthquake or the acidity of a liquid, in order to avoid the use of large numbers.

# Properties of Logarithms

Compute

$\log_{4}{1024}.$

Evaluate

$\log_\frac{1}{2} {\frac{1}{8}} + \log_\frac{1}{3} {3}.$

Evaluate $$9 ^ {\log_{9} 65}$$.

Evaluate $x = \log_3{\left(3\times 81^{\frac{1}{5}}\right)} - \log_9 \left[ {\left(\frac{1}{27}\right)^{\frac{1}{4}}} \right] + 3\log_{81}{9} .$

Evaluate $$\log_{10}{25} + \log_{10}{40}$$.

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