Equation with logarithms and absolute values I have this equation and I want to solve it for x<0. (ln|x|)/(|x|)=(ln|x|)/(x) According to WolframAlpha, the solution is x=−1 but I don't know how to get that.

klesstilne1

klesstilne1

Answered question

2022-11-09

Equation with logarithms and absolute values
I have this equation and I want to solve it for x < 0
ln | x | | x | = ln | x | x
According to WolframAlpha, the solution is x = 1 but I don't know how to get that.
My approach:
ln | x | | x | = ln | x | x
1 | x | = 1 x
| x | = x
x = x
2 x = 0
x = 0
which is apparently wrong. Where have I made the mistake?

Answer & Explanation

Aliya Moore

Aliya Moore

Beginner2022-11-10Added 17 answers

Hint
if x 1,
ln | x | x = ln | x | | x | 1 x = 1 | x |

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