1. Logarithm

write 1/2log a(x+2) - 3 log a(x-1) + 2 log a x as a single logarithm...

2. Originally Posted by cruxkitty
write 1/2log a(x+2) - 3 log a(x-1) + 2 log a x as a single logarithm...
$\frac{1}{2}\log_a(x+2)-3\log_a(x-1)+2\log_a(x)$

We know that $\log_c a-\log_c b=\log_c\bigg(\frac{a}{b}\bigg)$, $\log_c a+\log_c b=\log_c(ab)$, and $a\log_c b=\log_c(b^a)$

Thus, our expression becomes:

$\log_a(\sqrt{x+2})-\log_a((x-1)^3)+\log_a(x^2) = \log_a\bigg(\frac{\sqrt{x+2}}{(x-1)^3}\bigg)+\log_a(x^2)$
$=\color{red}\boxed{\log_a\bigg(\frac{x^2\sqrt{x+2} }{(x-1)^3}\bigg)}$

Hope this makes sense!

--Chris