what is the solution of $ln(x + 6)-ln9 = 2$? round your answer to the nearest hundredth.\n$x = 53.50$\n$x =…

Explanation:

Step1: Use logarithm property

By the property $\ln a-\ln b = \ln\frac{a}{b}$, we have $\ln\frac{x + 6}{9}=2$.

Step2: Convert to exponential form

Since $\ln y=x$ is equivalent to $y = e^{x}$, then $\frac{x + 6}{9}=e^{2}$.

Step3: Solve for x

Multiply both sides by 9: $x+6 = 9e^{2}$. Then $x=9e^{2}-6$. We know that $e\approx2.7183$, so $e^{2}\approx7.3891$. Then $x=9\times7.3891 - 6=66.5019-6=60.5019\approx60.50$.

Answer:

$x = 60.50$