Solve: $\log _ { 32 } x = \frac { 2 } { 5 }$
A) $\{ 4 \}$
B) $\{ - 8 \}$
C) $\{ 8 \}$

D) no solution

Name: Solve: $\log _ { 32 } x = \frac { 2 } { 5 }$ A) $\{ 4 \}$ B) $\{ - 8 \}$ C) $\{ 8 \}$ D) no solution
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Question

Solve: $\log _ { 32 } x = \frac { 2 } { 5 }$
A) $\{ 4 \}$
B) $\{ - 8 \}$
C) $\{ 8 \}$

D) no solution

Quizplus · Accepted Answer

The equation $\log _ { 32 } x = \frac { 2 } { 5 }$ can be rewritten using the definition of logarithms as $32^{\frac{2}{5}} = x$. Since $32 = 2^5$, this becomes $(2^5)^{\frac{2}{5}} = 2^{5*\frac{2}{5}} = 2^2 = 4$. Therefore, $x = 4$, which corresponds to choice A.

Solve log⁡32x=25\log _ { 32 } x = \frac { 2 } { 5 }log32​x=52​

Solve $\log _ { 32 } x = \frac { 2 } { 5 }$