Solve the given equation for x. $$7 = 6 + 4 e ^ { - 5 x }$$
A) $- 5 e ^ { 4 }$
B) $- \frac { e ^ { 4 } } { 5 }$
C) $- \frac { \ln 4 } { 5 }$
D) $\frac { \ln 4 } { 5 }$

Question

Quizplus · Accepted Answer

First, isolate the exponential term: $4e^{-5x} = 7 - 6 = 1$. Then, divide by 4: $e^{-5x} = \frac{1}{4}$. Taking the natural logarithm of both sides gives $-5x = \ln(\frac{1}{4})$, which simplifies to $-5x = \ln(1) - \ln(4) = -\ln(4)$. Solving for $x$ gives $x = \frac{-\ln(4)}{-5} = \frac{\ln(4)}{5}$.

Solve the Given Equation for X 7=6+4e−5x7 = 6 + 4 e ^ { - 5 x }7=6+4e−5x

Solve the Given Equation for X $7 = 6 + 4 e ^ { - 5 x }$