Question

solve 3log 2x = 4 . Round to the nearest thousandth

Answer 1

Is it \(3\log(2x)=4\) Or \(3\log_2(x)=4\)?

Answer 2

Either way,\[3\log(2x)=4 \]\[\log(2x)=\frac{4}{3}\]\[e^{\log(2x)}=e^{4/3}\]\[2x=e^{2x}\]solve for x.

Answer 3

\[3\log_2(x)=4\]\[\log_2(x)^3=4\]Change of base: \(\log_a (x)\implies \dfrac{\log(x)}{\log(a)}\) \[\log_2(x)^2= 4 \implies \frac{3\log(x)}{\log(2)}=4\] Solve for x.