Question

Rewrite the following expression in logarithmic form and use that to solve for the variable. Show all work done in this process. 2ex = 6

Answer 1

`ln(e^x)=ln(3)`

`x=1.099`

Explanation:

You have the following exponential expression:

`2e^x=6`

You need to divide both sides of the equation by 2:

`(2e^x)/(2)=(6)/(2)\\\\e^x=3`

Now apply the function Natural logarithm to both sides of the function:

`ln(e^x)=ln(3)`

Note that now the exponential function is transformed into a logarithmic function.

By definition:

`ln(e^x)=x` Because the base of the Natural logarithm is the Euler's number "e".

Then you can solve for "x":

`x=ln(3)\\x=1.099`)