Question

PLEASE HELP ME

27
What is the exact solution to the equation
e^3x+5=9 ?


x=3/5+in9


x=3/ln9−5


x=5+ln9/3


x=ln9−5/3

Answer 1

`x=(-5+ln9)/(3)` which appears to be from the list x=ln9-5/3

Explanation:

We take the natural logarithm of both sides as the inverse operation to an exponent on e. This allows us to use log rules to rearrange the problem.

`e^(3x+5)=9\\lne^(3x+5)=ln9 \\(3x+5)lne=ln9`

We know that as inverse operations, ln e =1.

`(3x+5)(1)=ln9\\3x+5=ln9\\3x=-5+ln9\\(3x)/(3)=(-5+ln9)/(3)`

`x=(-5+ln9)/(3)`

Answer 2

x = (ln (9)-5) /3

Explanation:

e^3x+5=9

First we subtract 5 from each side

e^3x+5-5=9-5

e^3x=(9-5)

Then we take the natural log of each side

ln(e^3x) = ln(9-5)

3x = ln (9-5)

Then we divide by 3 on each side

3x/3 = ln (9-5) /3

x = ln (9-5) /3