Question

What is the true solution to 2 In 4x=2 In 8

Answer 1

divide by two

ln is base e. both sides of the equation are base e so the parts inside the parentheses are equal

x=2

Answer 2

`x=2` is the true solution.

Explanation:

We have been given the expression:

`2\ln 4x=2\ln 8`

Using:

`n\ln m=\ln m^n`

Our given expression becomes:

`ln(4x)^2=ln(8^2)`

Cancel ln from both sides we get:

`4x^2=8^2`

On simplification we get:

`16x^2=64`

`x^2=4`

Final simplification gives the result:

`x=2`