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:  $\log_{10} 8 = \log_{10} 2^3 = 3\log_{10} 2$ and $\log_{10} 9 = \log_{10} 3^2 = 2\log_{10} 3$. 
