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Use logarithms to evaluate 3/(86.37 x 6.285).

Mathematics

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Step 1: Set up the logarithmic expression.
Let X=38.32×12.96486.37×6.2853X = \sqrt[3]{\frac{38.32 \times 12.964}{86.37 \times 6.285}}.
Taking the logarithm of both sides:

log⁡X=log⁡((38.32×12.96486.37×6.285)13)\log X = \log \left( \left( \frac{38.32 \times 12.964}{86.37 \times 6.285} \right)^{\frac{1}{3}} \right)

Using logarithm properties log⁡(ab)=blog⁡a\log(a^b) = b \log a and log⁡(ab)=log⁡a−log⁡b\log(\frac{a}{b}) = \log a - \log b:

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