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

Question

Quizplus · Accepted Answer

The expression $\log _ { 7 } \sqrt [ 3 ] { 49 }$ can be simplified by recognizing that $49 = 7^2$. Therefore, $\sqrt [ 3 ] { 49 } = \sqrt [ 3 ] { 7^2 }$. This can be rewritten as $7^{2/3}$. The logarithm $\log _ { 7 } 7^{2/3}$ simplifies to $2/3$, because the base of the logarithm and the base of the exponent are the same, so the answer is simply the exponent, which is $\frac { 2 } { 3 }$.

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

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