Question

The value of ${\log }_{\frac{1}{3}}\sqrt[4]{4729\sqrt[3]{39^{-1}{27}^{-\frac{4}{3}}}}$ is

• A. $1$
• B. $-1$
• C. $3$
• D. $\frac{1}{3}$

Answer 1

Answer: (B)

$-1$

${\log }_{\frac{1}{3}}\sqrt[4]{4729\left(\sqrt[3]{39^{-1}{27}^{-\frac{4}{3}}}\right)}$
$={\log }_{\frac{1}{3}}\sqrt[4]{4729\left(\sqrt[3]{33^{-2}{3}^{-4}}\right)}$
$={\log }_{\frac{1}{3}}\sqrt[4]{4729\left(3^{-2}\right)}={\log }_{\frac{1}{3}}\sqrt[4]{43^4}={\log }_{\frac{1}{3}}3=-{\log }_{3}3=-1,[\because {\log }_{a}a=1]$