Help with a logarithm proof

Question

If $$\log \frac {1} {2} (a + b) = \frac {1} {2}(\log (a) + \log (b) )$$ Prove that $$ (a + b)^2 = 4ab $$

Can anyone show me how to do this?

Thanks.

Answer 1

$$2 \ln \left(\frac{1}{2} (a + b)\right) = \ln a + \ln b$$

$$\ln \left(\frac{1}{4} (a+b)^2\right) = \ln (ab)$$

$$(a+b)^2 = 4ab$$