Question

If $(\sqrt[3]{34}{)}^{2x+\frac{1}{2}}=\frac{1}{32}$, then x = ____.

• A. $-2$
• B. $4$
• C. $-6$
• D. $-4$

Answer 1

The correct option is D $-4$

$(3\sqrt{4}{)}^{2x+1/2}=\frac{1}{32}$

$\Rightarrow 2^{2/3}(2x+\frac{1}{2})=2^{-5}$

$\Rightarrow 4x+1=-15$

$\Rightarrow x=-4$