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?

Hint. It's a bit confusing with your notation, but you can use the fact that
$$
\log_9 8 \times \log_2 3 = \log_9 8^{\log_2 3}
$$
and observe that
$$
8 = 2^3
$$
It will also be useful to know that (in this context)
$$
(a^b)^c = (a^c)^b
$$
