I need to compare those two expressions and decide which is bigger.
$2 \sqrt2$ or $\log_2(3)+\log_3(4) $.
So I tried to simplify so the log expression so I know
and so
$$ \log_2(4) \times (\log_4(3) + \log_3(2)) ?? 2 \times \sqrt2$$
and then
$$2 \times \log_2(2)\times(\log_4(3)+\log_3(2)) ?? 2 \sqrt2$$
$$\log_2(2) \times (\log_4(3)+\log_3(2)) ?? \sqrt2 $$
and I know $\ log_2(2) = 1$ so now I need to compare those two expressions:
$$\log_4(3)+\log_3(2) $$against$$ \sqrt2 $$
I'm not really sure what i'm doing wrong here.