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

Answer:

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

$x=1.099$

Step-by-step explanation:

You have the following exponential expression:

$2e^x=6$

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

$\frac{2e^x}{2}=\frac{6}{2}\\\\e^x=3$

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":

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