Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$5 ^ { x + 6 } = 2$$
A) $\left\{ \frac { \ln 2 } { \ln 5 } - 6 \right\}$
B) $\left\{ \frac { \ln 5 } { \ln 2 } + 6 \right\}$
C) $\left\{ \frac { \ln 5 } { \ln 2 } + \ln 6 \right\}$
D) $\{ \ln 2 - \ln 5 - \ln 6 \}$

Question

Quizplus · Accepted Answer

To solve $5^{x+6} = 2$, take the natural logarithm of both sides to get $\ln(5^{x+6}) = \ln(2)$. Using the property of logarithms that allows the exponent to be brought in front, we get $(x+6)\ln(5) = \ln(2)$. Solving for $x$ gives $x = \frac{\ln(2)}{\ln(5)} - 6$, which matches choice A.

Solve the Exponential Equation 5x+6=25 ^ { x + 6 } = 25x+6=2

Solve the Exponential Equation $5 ^ { x + 6 } = 2$