How do I solve this logarithmic equation? the equation is ln &#x2061;<!-- ⁡ --> ( x

Caleb Proctor

Caleb Proctor

Answered question

2022-07-14

How do I solve this logarithmic equation?
the equation is
ln ( x + 2 ) = ln e ln 2 ln x
How do I solve for x?

Answer & Explanation

Dalton Lester

Dalton Lester

Beginner2022-07-15Added 12 answers

Your equation is equivalent to
ln ( x + 2 ) + ln ( x ) = ln 2.
Then use logarithm identity ln a b = ln a + ln b$
ln ( x + 2 ) x = ln 2.
Now take inverse of both sides
( x + 2 ) x = 2.
Now you can solve the quadratic equation and select the appropriate x value. You get x = 1 ± 3 .. Note that you can not take x < 0 as ln x is not defined for negative x. So your answer is x = 1 + 3 which is approximately equal to 0.732

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