Question

Solve for x, where x is a real number
4e^2x=12

could any1 please explain how to solve this step by step. I really want to be able to understand this.

Is the answer even a real number?

Answer 1

\(\large\color{blue}{4e^{2x}=12 \LARGE\color{white}{ \rm │ }}\)
\(\large\color{blue}{e^{2x}=3 \LARGE\color{white}{ \rm │ }}\)
\(\large\color{blue}{\ln(e^{2x})=\ln(3) \LARGE\color{white}{ \rm │ }}\)
\(\large\color{blue}{2x\ln(e)=\ln(3) \LARGE\color{white}{ \rm │ }}\) ( `ln(e)=1` )
\(\large\color{blue}{2x=\ln(3) \LARGE\color{white}{ \rm │ }}\)
\(\large\color{blue}{x=\ln(3)\div 2 \LARGE\color{white}{ \rm │ }}\)

Answer 2

divide by 4

e^2x = 3

take loges (base e)

2x = ln3

you got it?...

Answer 3

thanks guys, i got it now :)

Answer 4

You can play around with \(\large\color{blue}{x=\ln(3)\div 2 \LARGE\color{white}{ \rm │ }}\)

\(\large\color{blue}{x=\ln(3)\div 2 \LARGE\color{white}{ \rm │ }}\)
\(\large\color{blue}{x=\ln(3)\div 2\ln(e) \LARGE\color{white}{ \rm │ }}\)
\(\large\color{blue}{x=\ln(3)\div \ln(e^2) \LARGE\color{white}{ \rm │ }}\)
\(\large\color{blue}{x=\ln(3-e^2) \LARGE\color{white}{ \rm │ }}\)