Question

1. Se P=$\sqrt[3]{ab^2}$, Calcule log P.

2. Dados Log a = 5, Log b = 3 e log c = 2, calcule o valor de log$(\frac{ab^2}{c})$

Answer 1

1)

$log~P=log~\sqrt[3]{ab^{2}}\\\\log~P=log~(ab^{2})^{\frac{1}{3}}\\\\log~P=\frac{1}{3}\cdot log~(ab^{2})\\\\log~P=\frac{1}{3}\cdot(log~a+log~b^{2})\\\\log~P=\frac{1}{3}\cdot(log~a+2\cdot log~b)\\\\\\\boxed{\boxed{log~P=\frac{1}{3}\cdot log~a+\dfrac{2}{3}\cdot log~b}}$
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2)

$log~(\frac{ab^{2}}{c})=log~a+log~b^{2}-log~c\\\\log~(\frac{ab^{2}}{c})=5+2\cdot log~b-2\\\\log~(\frac{ab^{2}}{c})=3+2\cdot3\\\\log~(\frac{ab^{2}}{c})=3\cdot3\\\\\\\boxed{\boxed{log~\left(\frac{ab^{2}}{c}\right)=9}}$