Question

Logaritmo
log2/√3 (9/16)

Answer 1

$log_{\frac{2}{\sqrt3}}(\frac{9}{16})=x \Rightarrow (\frac{2}{\sqrt3})^x=\frac{9}{16}\\ \\ (\frac{2}{\sqrt3})^x=(\frac{16}{9})^{-1}\\ \\ (\frac{2}{\sqrt3})^x=\left(\frac{2^4}{(\sqrt3)^4}\right)^{-1}\\ \\ (\frac{2}{\sqrt3})^x=(\frac{2}{\sqrt3})^{-4}\\ \\ \boxed{x=-4}$

Answer 2

Aplicando propriedades operatórias de logaritmos

$log (\frac{2}{ \sqrt{3} } ) \frac{9}{16} =p \\ \\ \frac{9}{16} =( \frac{2}{ \sqrt{3} } )^p \\ \\ ( \frac{16}{9}) ^{-1} =( \frac{2}{ \sqrt{3} })^p \\ \\ ( \frac{2^4}{3^2.3^2.3 ^{ \frac{1}{2} } } ) ^{-1} =( \frac{2}{ \sqrt{3} })^p$

$[( \frac{2}{ \sqrt{3} })^4] ^{-1} = (\frac{2}{ \sqrt{3} })^p \\ \\ ( \frac{2}{ \sqrt{3} } ) ^{-4} = ( \frac{2}{ \sqrt{3} })^p \\ \\ p = -4$