Question

$\sqrt[3]{35^{\frac{1}{{\log }_{7}5}}+\frac{1}{\sqrt{-{\log }_{10}\left(0.1\right)}}}=$

• A. $0$
• B. $2$
• C. $1$
• D. does not exist

Answer 1

The correct option is B $2$

$5^{\frac{1}{{\log }_{7}5}}=5^{{\log }_{5}7}=7(\because a^{{\log }_{a}b}=b)\sqrt{-{\log }_{10}\left(0.1\right)}=\sqrt{{\log }_{10}\left(10\right)}=1$

$\therefore \sqrt[3]{35^{\frac{1}{{\log }_{7}5}}+\frac{1}{\sqrt{-{\log }_{10}\left(0.1\right)}}}$
$=\sqrt[3]{37+1}=\sqrt[3]{38}=2$