Solve the following equation for . $\ln ( x - 5 ) ^ { 5 } = 3$
A) $x = 8$
B)$x = e ^ { \sqrt [ 5 ] { 3 } } + 5$
C) $x = \frac { 3 } { \ln ( 5 ) ^ { 5 } }$
D)$x = e ^ { \frac { 3 } { 5 } } + 5$
E) no solution

Question

Quizplus · Accepted Answer

To solve the equation $\ln ( x - 5 ) ^ { 5 } = 3$, we first rewrite it as $( x - 5 ) ^ { 5 } = e^3$. Taking the fifth root of both sides gives $x - 5 = e^{3/5}$. Adding 5 to both sides gives $x = e^{3/5} + 5$.

Solve the Following Equation for ln⁡(x−5)5=3\ln ( x - 5 ) ^ { 5 } = 3ln(x−5)5=3

Solve the Following Equation for $\ln ( x - 5 ) ^ { 5 } = 3$