Solve this logarithmic equation: 2^(2- ln x)+2^(2+ ln x)=8

Aarav Atkins

Aarav Atkins

Answered question

2022-10-22

Solve this logarithmic equation: 2 2 ln x + 2 2 + ln x = 8. I thought to write
2 2 2 ln ( x ) + 2 2 2 ln ( x ) = 2 3 2 2 + 2 2 ( 2 ln ( x ) ) 2 2 ln ( x ) = 2 3
What should I do else?

Answer & Explanation

wespee0

wespee0

Beginner2022-10-23Added 15 answers

We have 2 2 ln ( x ) = 4 2 ln ( x ) and 2 2 + ln ( x ) = 4 2 ln ( x ) . Hence, setting 2 ln ( x ) = a, we obtain
4 a + 4 a = 8 a 2 + 1 = 2 a a = 1 2 ln ( x ) = 1 x = 1
Maribel Vang

Maribel Vang

Beginner2022-10-24Added 2 answers

Hint:
Dividing by 4 we get the equivalent equation
2 ln x + 2 ln x = 2
then let y = 2 ln x so
y 1 + y = 2 1 + y 2 = 2 y

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