Solve the equation. Round to the nearest thousandth.
-$$3 ^ { ( x + 6 ) } = 4 ^ { x }$$
A) $\{ - 22.913 \}$
B) $\{ 21.313 \}$
C) $\{ 24.513 \}$
D) $\{ 22.913 \}$

Question

Quizplus · Accepted Answer

Taking the natural logarithm of both sides of the equation gives:$$\ln(3^{x+6}) = \ln(4^x)$$Using the properties of logarithms, we can simplify this to:$$(x+6)\ln(3) = x\ln(4)$$Solving for x, we get:$$x = \frac{6\ln(3)}{\ln(4) - \ln(3)} \approx 22.913$$Therefore, the correct answer is D) $ \{ 22.913 \}$.

Solve the Equation 3(x+6)=4x3 ^ { ( x + 6 ) } = 4 ^ { x }3(x+6)=4x

Solve the Equation $3 ^ { ( x + 6 ) } = 4 ^ { x }$