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 $\log _ { 7 } \sqrt [ 3 ] { 49 }$ simplifies to $\log _ { 7 } 7^{2/3}$, which equals $\frac { 2 } { 3 }$ because the base and the argument have the same base (7), making the exponent the value of the logarithm.

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

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