Find the exact value of $\log _ { 5 } \sqrt [ 3 ] { 25 }$ without using a calculator.
A) $\frac { 25 } { 3 }$
B) $\frac { 3 } { 25 }$
C) $\frac { 10 } { 3 }$
D) $\frac { 2 } { 3 }$
E) $- 1$

Question

Quizplus · Accepted Answer

The expression can be simplified as $\log_5(25^{1/3})$. Since $25 = 5^2$, this becomes $\log_5((5^2)^{1/3})$, which simplifies to $\log_5(5^{2/3})$. By the properties of logarithms, this equals $\frac{2}{3}$.

Find the Exact Value Of log⁡5253\log _ { 5 } \sqrt [ 3 ] { 25 }log5​325​

Find the Exact Value Of $\log _ { 5 } \sqrt [ 3 ] { 25 }$