Let's find x.
[tex]\text{ 9(6}^{3x})\text{ }=\text{ 24}[/tex]
We get,
[tex]\text{ 9(6}^{3x})\text{ }=\text{ 24}[/tex][tex]\frac{9\cdot\:6^{3x}}{9}=\frac{24}{9}[/tex][tex]6^{3x}=\frac{8}{3}[/tex]
Applying the rules of exponent, we get:
[tex]3x\ln \mleft(6\mright)=\ln \mleft(\frac{8}{3}\mright)[/tex][tex]x=\frac{\ln(\frac{8}{3})}{3\ln(6)}\text{ = }0.18247\ldots[/tex][tex]x\text{ }\approx\text{ 0.182}[/tex]
Therefore, the answer is 0.182
