Answer
$b=e^2$
Work Step by Step
$f(x)=\log _{b}\left(3 x^{2}-2\right)\\
f^{\prime}(x)=\frac{1}{\left(3 x^{2}-2\right) \ln b} \times 6 x\\
f^{\prime}(x)=\frac{6 x}{\left(3 x^{2}-2\right) \ln b}\\
3=\frac{6(1)}{\left(3(1)^{2}-2\right) \ln b}\\
\ln b=2\\
b=e^2$
