Find the exact value of $\log _ { 7 } \sqrt [ 3 ] { 49 }$ without using a calculator.
A) $\frac { 49 } { 3 }$
B) $\frac { 3 } { 49 }$
C) $\frac { 14 } { 3 }$
D) $\frac { 2 } { 3 }$
E)-1

Question

Quizplus · Accepted Answer

The expression can be simplified as $\log_7(49^{\frac{1}{3}})$. Since $49 = 7^2$, this becomes $\log_7((7^2)^{\frac{1}{3}})$ or $\log_7(7^{\frac{2}{3}})$. By the properties of logarithms, this simplifies to $\frac{2}{3}$.

Find the Exact Value Of log⁡7493\log _ { 7 } \sqrt [ 3 ] { 49 }log7​349​

Find the Exact Value Of $\log _ { 7 } \sqrt [ 3 ] { 49 }$