Answer
$x \approx 1.71$
Work Step by Step
RECALL:
$\ln{a^b} = b \cdot \ln{a}$
Take the natural logarithm of both sides to obtain:
$\ln{4^{x+1}}=\ln{9^x}$
Use the rule above to obtain:
$(x+1)\ln{4}=x\ln{9}$
Distribute $\ln{4}$ to obtain:
$x\ln{4} + \ln{4} = x\ln9$
Subtract $\ln{4}$ on both sides to obtain:
$x\ln{4} = x\ln{9}-\ln{4}$
Subtract $x\ln{9}$ on both sides of the equation to obtain:
$x\ln{4} - x\ln{9}=-\ln{4}$
Factor out $x$ on the left side of the equation to obtain:
$x(\ln4-\ln9)=-\ln{4}$
Divide $(\ln{4} - \ln{9})$ on both sides of the equation to obtain:
$x = \dfrac{-\ln{4}}{\ln{4}-\ln{9}}$
Use a scientific calculator to obtain:
$x= 1.709511291
\\x \approx 1.71$
