Answer
$1$
Work Step by Step
The given expression can be written as:
$5 (1.2)^{3x-2}=6 $
or, $(1.2)^{3x-2}=\dfrac{6}{5}$
We need to take log of both sides and apply logarithmic property : $\log a^ b=b \log a$ .
$(3x-2) \log (1.2)=\log \dfrac{6}{5}$
Now, we will evaluate the result for $x$.
$x=\dfrac{\dfrac{\log \dfrac{6}{5}}{\log 1.2 }+2}{3}$
Now, apply logarithmic property : $\log \dfrac{a}{b}=\log a - \log b$ .
$x=\dfrac{\dfrac{\log 6 - \log 5}{\log 1.2}+2}{3}$
Therefore, our answer is: $x=\dfrac{1+2}{3}=1$