# Math Help - Logarithm

1. ## Logarithm

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

2. Use the following rules:

$log_{a}x + log_{a}y = log_{a}xy$

$log_{a}x - log_{a}y = log_{a}\frac{x}{y}$

$\alpha \cdot log_{a}x = log_{a}x^\alpha$

3. Surely you know something about it, otherwise you would not ahve such an assignment. What are your thoughts?

log(a) + log(b) = log(a*b)

There are other rules. Use them.

4. Originally Posted by katchat64
Write 1/2 log a (x + 2) - 3 log a (x - 1) + 2 log a X as a single logarithm.
$\frac{1}{2} \log_a(x+2) - 3 \log_a(x-1) + 2 \log_a(x)$
$=\log_a(x+2)^\frac{1}{2} - \log_a(x-1)^3 + \log_a(x)^2$
$=\log_a \left [ \frac{(x+2)^\frac{1}{2}}{(x-1)^3} \right ] + \log_a(x)^2$
$=\log_a \left [ \frac{x^2(x+2)^\frac{1}{2}}{(x-1)^3} \right ]$