How to simplify the expression $(\log_9 2 + \log_9 4)\log_2 (3)$ Our test asked to simplify $(\log_9 2 + \log_9 4)\log_2 (3)$.
I simplified the first parenthesis to be $\log_9 (8)$.
So, now I have $\log_9 (8) \cdot \log_2 (3)$ and I can change to base $10$ and get, $$\frac{\log 8}{\log 9} \cdot \frac{\log 3}{\log 2}$$ However, the problem shows that this should without a calculator simplify to $1.5$.  Without using a calculator, I don't see how I'm supposed to get $3/2$ from the multiplication of these $2$ logs.  Any thoughts?

$$(\log_{9}2+\log_9{4})\log_{2}3$$
this equal to:
$$\log_{9}8\cdot \log_{2}3=\frac{3\log2}{2\log3}\cdot\frac{\log3}{\log2}=\frac{3}{2}$$
