## College Algebra (6th Edition)

$$\frac{1}{2}(A-3C)$$
$\log_b2=A$ and $\log_b3=C$ $$X=\log_b\sqrt{\frac{2}{27}}$$ $$X=\log_b\Bigg(\frac{2}{27}\Bigg)^{1/2}$$ Apply the Power Rule here, we can move the exponent $1/2$ away for Quotient Rule usage later. $$X=\frac{1}{2}\log_b\frac{2}{27}$$ Now we can apply Quotient Rule for $\log_b\frac{2}{27}$ $$X=\frac{1}{2}(\log_b2-\log_b27)$$ $$X=\frac{1}{2}(\log_b2-\log_b3^3)$$ Again, use the Power Rule for $\log_b3^3$ $$X=\frac{1}{2}(\log_b2-3\log_b3)$$ Now we substitute A and C into X $$X=\frac{1}{2}(A-3C)$$