Question

solve the equation analytically.

Answer 1

\[4^{2x}=\frac{ 1 }{ 2 }\]

Answer 2

\[2xlog4=\log \frac{ 1 }{ 2 }\]

Answer 3

what can i do next in orfer to solve for the x dont i need a base

Answer 4

the base is already 10 by default

Answer 5

actually by default, it can either be "e" or "10"
generally, we take "e" if nothing is mentioned.

Answer 6

\[4^{2x} =\frac{ 1 }{ 2 }\]You could do this:\[\ln(4^{2x})=\ln(\frac{ 1 }{ 2 }) \rightarrow 2xln(4)=\ln(\frac{ 1 }{ 2 }) \rightarrow 2x=\frac{ \ln \frac{ 1 }{ 2 } }{ \ln(4) }\]\[x=2(\frac{ \ln \frac{ 1 }{ 2 } }{ \ln(4) })\]

Answer 7

well, the question doesn't have logs given to us in the first place.
so its our choice to take whatever base we want to of the log
base 2 would be ideal here.

Answer 8

@Lynncake the answer equals to \[x=-\frac{ 1 }{ 4 }\] i see whereyou got the 1/4 but how can i pull the negative

Answer 9

got it....