Solving a simple exponential equation How can I solve this logarithm: e <mrow class

Eden Solomon

Eden Solomon

Answered question

2022-06-15

Solving a simple exponential equation
How can I solve this logarithm:
e 2 x 3 e x + 2 = 0.
I think it should be re-written as a quadratic equation in e x

Answer & Explanation

zalitiaf

zalitiaf

Beginner2022-06-16Added 27 answers

e 2 x 3 e x + 2 = 0
let e x = y
y 2 3 y + 2 = 0
y 2 2 y y + 2 = 0
y ( y 2 ) 1 ( y 2 ) = 0
( y 2 ) ( y 1 ) = 0
( y 2 ) = 0 , ( y 1 ) = 0
y = 2 , 1
e x = 2 , e x = 1
log e e x = log e 2 , log e e x = log e 1
x = log e 2 , x = 0
Checking the answer:
e 2 x 3 e x + 2 = 0
x = log e 2 put this value in eqn.
e 2 log e 2 3 e log e 2 + 2 = 0 e log e 2 2 3 e log e 2 + 2 = 0 4 6 + 2 = 0 s a t i s f y
x=0 put this value in eqn.
e 0 3 e 0 + 2 = 0 1 3 + 2 = 0 s a t i s f y
so both answer are correct.
Jackson Duncan

Jackson Duncan

Beginner2022-06-17Added 10 answers

You can also factor the expression directly as ( e x 1 ) ( e x 2 )

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