Question

Evaluate rge following logarithmic expression without the use of a calculator.Enter your answer as a fraction reduced to lowest terms. log8(7√64)

Answer 1

$\bf log_8(\sqrt[7]{64})\qquad 64=8^2\qquad log_8(\sqrt[7]{8^2})\\\\ -----------------------------\\\\ log_{{ a}}{{ a}}^x\implies x\impliedby \textit{using this cancellation rule}\\\\ -----------------------------\\\\ log_8\left( 8^{\frac{2}{7}} \right)\implies \cfrac{2}{7}$