x = 3.40 ( to the nearest hundredth)
Explanations:The given equation is:
[tex]3^x=\text{ 42}[/tex]Take the logarithm to base 10 of both sides.
The equation becomes:
[tex]\begin{gathered} \log 3^x=\text{ log 42} \\ x\text{ log 3 = log 42} \\ x\text{ = }\frac{\log \text{ 42}}{\log \text{ 3}} \\ x\text{ = }\frac{1.623}{0.477} \\ x\text{ = }3.40 \end{gathered}[/tex]