Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$4 ^ { x + 6 } = 7$$
A) $\left\{ \frac { \ln 4 } { \ln 7 } + \ln 6 \right\}$

B) $\{ \ln 7 - \ln 4 - \ln 6 \}$

C) $\left\{ \frac { \ln 7 } { \ln 4 } - 6 \right\}$

D) $\left\{ \frac { \ln 4 } { \ln 7 } + 6 \right\}$

Question

Solve the exponential equation. Express the solution set in terms of natural logarithms.
-$$4 ^ { x + 6 } = 7$$
A) $\left\{ \frac { \ln 4 } { \ln 7 } + \ln 6 \right\}$

B) $\{ \ln 7 - \ln 4 - \ln 6 \}$

C) $\left\{ \frac { \ln 7 } { \ln 4 } - 6 \right\}$

D) $\left\{ \frac { \ln 4 } { \ln 7 } + 6 \right\}$

Quizplus · Accepted Answer

To solve the equation $4^{x+6} = 7$, we first take the natural logarithm of both sides to get $\ln(4^{x+6}) = \ln(7)$. Using the property of logarithms that allows us to bring the exponent down ($\ln(a^b) = b\ln(a)$), we get $(x+6)\ln(4) = \ln(7)$. Solving for $x$, we get $x = \frac{\ln(7)}{\ln(4)} - 6$, which matches choice C.

Solve the Exponential Equation 4x+6=74 ^ { x + 6 } = 74x+6=7

Solve the Exponential Equation $4 ^ { x + 6 } = 7$