(ln(x^2))/(ln(x)) = 2? Why?

Elliana Molina

Elliana Molina

Answered question

2022-11-11

ln ( x 2 ) ln ( x ) = 2? Why?
Upon trying to evaluate ln ( x 2 ) ln ( x ) , i've found that google plots it as always equal to 2, other than 0 where it is undefined. Why is this the case?

Answer & Explanation

Savanna Smith

Savanna Smith

Beginner2022-11-12Added 17 answers

Recall the logarithm property
ln x 2 ln x = 2 ln x ln x = 2.
But this is only true when x > 0 and x 1. Otherwise, there is a "hole" there; a removable discontinuity. Notice that this is difficult not to graph, so graphing tools usually just fill the hole/graph over it.
Uriel Hartman

Uriel Hartman

Beginner2022-11-13Added 2 answers

ln ( x 2 ) ln ( x ) = 2 ln ( x ) ln ( x ) = 2

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