Question

Solve: ${\log }_4\sqrt[3]{38^{(3+\frac{1}{3}{\log }_{2}x)}}=0$

• A. $2^{-3}$
• B. $2^5$
• C. $2^{10}$
• D. $2^{-9}$

Answer 1

The correct option is D $2^{-9}$

Given expression is

$lo{g}_4(8^{(3+\frac{1}{3}lo{g}_{2}x{)}^{\frac{1}{3}})}=0$

$\frac{1}{3}lo{g}_4\left(8^3{.2}^{3\times \frac{1}{3}lo{g}_{2}x}\right)=0$

$\to \frac{log\left(8^3\right)+log\left(2^{lo{g}_{2}x}\right)}{log4}=0$

$\to 9log2+lo{g}_{2}x\left(log2\right)=0$

$9log2+\frac{logx}{log2}\times log2=0$

$\to 9log2+logx=0\to logx=-9log2\to logx=log\left(2^{-9}\right)$

we get $x=2^{-9}$