Answer:
[tex]ln(e^x)=ln(3)[/tex]
[tex]x=1.099[/tex]
Step-by-step explanation:
You have the following exponential expression:
[tex]2e^x=6[/tex]
You need to divide both sides of the equation by 2:
[tex]\frac{2e^x}{2}=\frac{6}{2}\\\\e^x=3[/tex]
Now apply the function Natural logarithm to both sides of the function:
[tex]ln(e^x)=ln(3)[/tex]
Note that now the exponential function is transformed into a logarithmic function.
By definition:
[tex]ln(e^x)=x[/tex] Because the base of the Natural logarithm is the Euler's number "e".
Then you can solve for "x":
[tex]x=ln(3)\\x=1.099[/tex])
