Find the exact value of $\log _ { 8 } \sqrt [ 3 ] { 64 }$ without using a calculator.
A) $\frac { 64 } { 3 }$
B) $\frac { 3 } { 64 }$
C) $\frac { 16 } { 3 }$
D) $\frac { 2 } { 3 }$
E) $- 1$

Question

Quizplus · Accepted Answer

The expression $\log _ { 8 } \sqrt [ 3 ] { 64 }$ simplifies to $\log _ { 8 } 4$, since $\sqrt [ 3 ] { 64 } = 4$. Since $8 = 2^3$ and $4 = 2^2$, we can rewrite the expression as $\log _ { 2^3 } 2^2$, which simplifies to $\frac { 2 } { 3 }$ by the change of base formula.

Find the Exact Value Of log⁡8643\log _ { 8 } \sqrt [ 3 ] { 64 }log8​364​

Find the Exact Value Of $\log _ { 8 } \sqrt [ 3 ] { 64 }$