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

Answer:

$x=\frac{-5+ln9}{3}$ which appears to be from the list x=ln9-5/3

Step-by-step 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.

$(3x+5)(1)=ln9\\3x+5=ln9\\3x=-5+ln9\\\frac{3x}{3}=\frac{-5+ln9}{3}$

$x=\frac{-5+ln9}{3}$

Answer 2

Answer:

x  = (ln (9)-5) /3

Step-by-step 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