When I try and solve the following I get the answer as log (x^-7/12)
1/3log(x^2) + log x - 3/4 log (x^3)
In the book it says log (x^1/12)
I agree with you ...
$\displaystyle \frac{1}{3}\log(x^2) + \log{x} - \frac{3}{4}\log(x^3)$
$\displaystyle \log(x^{\frac{2}{3}}) + \log{x} - \log(x^{\frac{9}{4}})$
$\displaystyle \log\left(\frac{x^{\frac{2}{3}} \cdot x}{x^{\frac{9}{4}}}\right)$
$\displaystyle \log\left(\frac{x^{\frac{5}{3}}}{x^{\frac{9}{4}}}\ right)$
$\displaystyle \log\left(\frac{x^{\frac{20}{12}}}{x^{\frac{27}{12 }}}\right)$
$\displaystyle \log\left(x^{-\frac{7}{12}}\right)
$
... books have been wrong before.