Question

If 2${}^x$ x 8 ${}^{1/5}$ = 2 ${}^{1/5}$, then x is equal to

• A. 1/5
• B. – 1/5
• C. 2/5
• D. 1
• E. – 2/5

Answer 1

The correct option is E

– 2/5

$\begin{array}{c}{2}^x\times 8^{1/5}=2^{1/5}\Rightarrow \frac{2^x\times 2^{3/5}}{2^{1/5}}=1\\ \Rightarrow 2^x.2^{\left(\frac{3}{5}-\frac{1}{5}\right)}=1\\ \Rightarrow 2^{\left(x+\frac{2}{5}\right)}=2^0\Rightarrow x+\frac{2}{5}=0\\ \therefore x=-\frac{2}{5}.\end{array}$