Solve the given equation for x. $6 = 5 + 9 e ^ { 3 x }$
A) $\frac { e ^ { 9 } } { 3 }$
B) $\frac { \ln 9 } { 3 }$
C) $- \frac { \ln 9 } { 3 }$
D) $3 e ^ { 9 }$

Question

Quizplus · Accepted Answer

First, isolate the exponential term: $9e^{3x} = 6 - 5 = 1$. Then, divide both sides by 9: $e^{3x} = \frac{1}{9}$. Taking the natural logarithm of both sides gives $3x = \ln\left(\frac{1}{9}\right)$, which simplifies to $3x = -\ln(9)$. Finally, divide by 3 to solve for $x$: $x = -\frac{\ln(9)}{3}$.

Solve the Given Equation for X 6=5+9e3x6 = 5 + 9 e ^ { 3 x }6=5+9e3x

Solve the Given Equation for X $6 = 5 + 9 e ^ { 3 x }$