Solve the equation. Write the solution set with the exact values given in terms of natural or common
logarithms. Also give approximate solutions to 4 decimal places, if necessary.
-$4 e ^ { 5 m - 5 } - 2 = 14$
A) $\left\{ \frac { \ln 4 + 5 } { 5 } \right\} ; m = 1.2773$
B) $\left\{ \frac { \ln 3 + 5 } { \ln 5 } \right\} ; m = 3.7893$
C) $\left\{ \frac { \ln 3 + 5 } { 5 } \right\} ; m = 1.2197$
D) $\left\{ \frac { \ln 4 + 5 } { \ln 5 } \right\} ; m = 3.9680$

Question

Quizplus · Accepted Answer

First, solve the equation $4e^{5m-5} - 2 = 14$ by adding 2 to both sides and dividing by 4, yielding $e^{5m-5} = 4$. Taking the natural logarithm of both sides gives $5m - 5 = \ln(4)$, and solving for $m$ gives $m = \frac{\ln(4) + 5}{5}$. Approximating this value gives $m \approx 1.2773$.

Solve the Equation 4e5m−5−2=144 e ^ { 5 m - 5 } - 2 = 144e5m−5−2=14

Solve the Equation $4 e ^ { 5 m - 5 } - 2 = 14$