How do I solve for x in ln &#x2061;<!-- ⁡ --> ( x ) ln &#x2061;<!-- ⁡ -->

kreamykraka80 2022-07-10 Answered
How do I solve for x in ln ( x ) ln ( x ) = 2 + ln ( x )
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Answers (2)

Alec Blake
Answered 2022-07-11 Author has 11 answers
HINT:
Putting ln ( x ) = y , , we get
y 2 y 2 = 0.
Do you know how to solve a Quadratic Equation?, and we know that
ln ( x ) = a x = e a .
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pouzdrotf
Answered 2022-07-12 Author has 4 answers
(1) ln ( x ) ln ( x ) = 2 + ln ( x ) ( ln ( x ) ) 2 ln ( x ) 2 = 0
Let t = ln x . Then (1) becomes
(2) t 2 t 2 = ( t 2 ) ( t + 1 ) = 0
So,
t = ln x = 2 x = e 2  or  t = ln x = 1 x = e 1 = 1 e
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