SOLUTION: The equation e^ { 2 x } - 11 e^ { x } +30 = 0 has two solutions. The smaller one is: and the larger one is:

Question 507911: The equation e^ { 2 x } - 11 e^ { x } +30 = 0 has two solutions.
The smaller one is:
and the larger one is:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The equation e^ { 2 x } - 11 e^ { x } +30 = 0 has two solutions.
The smaller one is:
and the larger one is:
**
e^ { 2 x } - 11 e^ { x } +30 = 0
e^2x-11^x+30=0
let u=e^x
u^2=e^2x
u^2-11u+30=0
(u-6)(u-5)=0
u=6
or
u=5
...
for u=6
e^x=6
take ln of both sides
lne^x=ln6
x=1.7918
..
for u=5
e^x=5
take ln of both sides
lne^x=ln5
x=1.6094
..
ans:
x=1.7918
and
x=1.6094
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