Answer
$x=\frac{10^{-.8}+2}{3}\approx.7195$
Work Step by Step
We are given the equation $\log(3x-2)=-.8$. To solve for x, remember that the base of a common logarithm is understood to be 10.
Therefore, $log(3x-2)=log_{10}(3x-2)=-.8$.
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x\gt0$ and every real number $y$.
Therefore, $3x-2=10^{-.8}$.
Add 2 to both sides.
$3x=10^{-.8}+2$
Divide both sides by 3.
$x=\frac{10^{-.8}+2}{3}\approx.7195$
