Solving for x in a equation involving natural logarithms How would I solve for x in this equation h

juanberrio8a

juanberrio8a

Answered question

2022-06-13

Solving for x in a equation involving natural logarithms
How would I solve for x in this equation here:
ln ( x ) + ln ( 1 / x + 1 ) = 3
I realize that the answer is e 3 1 , but I am not sure as to how to get it. Any input is appreciated.

Answer & Explanation

Esteban Johnson

Esteban Johnson

Beginner2022-06-14Added 15 answers

ln x + ln ( 1 x + 1 ) = ln ( x ( 1 / x + 1 ) ) = 3
ln ( x + 1 ) = 3 x + 1 = e 3 x = e 3 1
rose2904ks

rose2904ks

Beginner2022-06-15Added 3 answers

We know that l n ( a ) + l n ( b ) = l n ( a b )
Then, l n ( x ) + l n ( 1 x ) = l n ( x ( 1 x + 1 ) = l n ( 1 + x ) = 3
Now,
We know that e l n ( a ) = a
Then,
e l n ( 1 + x ) = e 3
This implies that
x + 1 = e 3 x = e 3 1

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