Question: If
$$a = \log\_23 , b = \log\_52$$
then what is $\log45$ ?

(I have to define $\log45$ using $a$ and $b$)

What I did :
$$\log45 = 2\log3 + \log5$$
$$\log45 = \log2\left(2a + \frac1{b}\right)$$

Stuck here. Please help me

Answer: 
You can proceed as follows:

$$ \log 2 = \frac{1}{\log \_2^{10}} = \frac{1}{\log\_2^2 + \log\_2^5} = \frac{1}{1+\frac{1}{b}}$$.
Try using these two identities:

$$a \log b = \log{b^a}$$

$$\log\_b a = \frac{\ln a}{\ln b}$$