Solve the given equation for x. $$0 = - 1 + 5 e ^ { - 7 x }$$
A) $- 7 e ^ { 5 }$
B) $- \frac { e ^ { 5 } } { 7 }$
C) $- \frac { \ln 5 } { 7 }$
D) $\frac { \ln 5 } { 7 }$

Question

Quizplus · Accepted Answer

First, add 1 to both sides to get $1 = 5e^{-7x}$. Then, divide both sides by 5 to get $\frac{1}{5} = e^{-7x}$. Taking the natural logarithm of both sides gives $\ln(\frac{1}{5}) = -7x$. Since $\ln(\frac{1}{5}) = \ln(1) - \ln(5) = -\ln(5)$, we have $-\ln(5) = -7x$. Solving for $x$ gives $x = \frac{\ln(5)}{7}$.

Solve the Given Equation for X 0=−1+5e−7x0 = - 1 + 5 e ^ { - 7 x }0=−1+5e−7x

Solve the Given Equation for X $0 = - 1 + 5 e ^ { - 7 x }$