Solve the given equation for x. $$10 = 9 + 8 e ^ { 9 x }$$
A) $9 e ^ { 8 }$
B) $\frac { e ^ { 8 } } { 9 }$
C) $\frac { \ln 8 } { 9 }$
D) $- \frac { \ln 8 } { 9 }$

Question

Quizplus · Accepted Answer

First, isolate the exponential term: $10 = 9 + 8e^{9x}$ becomes $1 = 8e^{9x}$ by subtracting 9 from both sides, then divide by 8 to get $e^{9x} = \frac{1}{8}$. Taking the natural logarithm of both sides gives $9x = \ln\left(\frac{1}{8}\right)$, which simplifies to $9x = -\ln(8)$. Finally, divide by 9 to solve for $x$, resulting in $x = -\frac{\ln(8)}{9}$.

Solve the Given Equation for X 10=9+8e9x10 = 9 + 8 e ^ { 9 x }10=9+8e9x

Solve the Given Equation for X $10 = 9 + 8 e ^ { 9 x }$