Question

Logarithm questions: how do I switch up the bases?

\[2 \log_{4} 9 - \log_{2} 3\]

Answer 1

\[\log_{a}b=1/(\log_{b}a) \]

Answer 2

but you dont hv to switch

Answer 3

\[2\log_2 3-\log_2 3\]

Answer 4

lets make some sense out of this

\[\log_4(x)=\frac{\log_2(x)}{\log_2(4)}\] by the change of base formula
and since \(\log_2(4)=2\) we get
\[\log_4(x)=\frac{1}{2}\log_2(x)\]

Answer 5

thanks!