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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.
Compute
\[\log_{4}{1024}.\]
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Evaluate
\[ \log_\frac{1}{2} {\frac{1}{8}} + \log_\frac{1}{3} {3}. \]
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Evaluate \(9 ^ {\log_{9} 65}\).
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Evaluate \[ x = \log_3{\left(3\times 81^{\frac{1}{5}}\right)} - \log_9 \left[ {\left(\frac{1}{27}\right)^{\frac{1}{4}}} \right] + 3\log_{81}{9} .\]
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Evaluate \(\log_{10}{25} + \log_{10}{40}\).
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