# Math Help - change of base on logs

1. ## change of base on logs

how does:

log base 4 of 3

become

log base 2 of root 3?

Im looking for the step by step please.

2. Originally Posted by 200001
how does:

log base 4 of 3

become

log base 2 of root 3?

Im looking for the step by step please.
Change of base rule: $\log_c{a} = \frac{\log_b{a}}{\log_b{c}}$

Power Rule: $k\, \log_b{a} = \log_b{a^k}$

$\log_4{3} = \frac{\log_2{3}}{\log_2{4}}$

Can you use those two rules to get the answer

Spoiler:
$\log_2{4} = 2$

$\frac{1}{2} \log_2{3} = \log_2{3^{1/2}} = \log_2{\sqrt{3}}$

3. Yes, awesome, thanks
i was missing my numerator on the half power and couldnt make the link between that and it becoming a power

Much appreciated