Question

Express in terms of log a, log b
$log((\sqrt[3]{3a^{-1}\sqrt{b^3}}÷\sqrt{b^3\sqrt{a}})$

Answer 1

$log\left(\sqrt{\frac{b^3}{a}÷}\sqrt{b^3}\sqrt{a}\right)$
$loglog(\frac{({b^3)}^{1/6}}{a^{1/3}}÷b^{3/2}{a}^{1/4})$
$log\left(\frac{b^{1/2}}{a^{1/3}{a}^{1/4}{b}^{3/2}}\right)$
$log\left(\frac{1}{a\frac{7}{12}b}\right)$
$({(a}^{-7/12}.b^{-1})=\frac{-17}{12}logo-logb$
$-(log{b}^{3/2}.a^{1/4})$
$(log{b}^{3/2}+log{a}^{1/4})$
$(3/2lo{g}^b+\frac{1}{4}loga)$
$-3/2lo{b}^b-\frac{1}{4}loga$