Find the sum of solutions to: 2 log_(4) ^2(|x+1|)+ log_4(|x^2-1|)+ log_(1/4)(|x-1|)=0 'm not sure about what to do with the absolute values, how can I get rid of them? Should I solve for all various cases depending on the sign of x+1 and x−1?

Juan Lowe

Juan Lowe

Answered question

2022-11-03

Find the sum of solutions to:
2 log 4 2 ( | x + 1 | ) + log 4 ( | x 2 1 | ) + log 1 4 ( | x 1 | ) = 0
I'm not sure about what to do with the absolute values, how can I get rid of them?
Should I solve for all various cases depending on the sign of x + 1 and x 1?

Answer & Explanation

Julius Haley

Julius Haley

Beginner2022-11-04Added 19 answers

Note that
log 1 / a x = log a x
so your equation becomes
2 ( log 4 | x + 1 | ) 2 + log 4 | x + 1 | + log 4 | x 1 | log 4 | x 1 | = 0
So
log 4 | x + 1 | ( 2 log 4 | x + 1 | + 1 ) = 0
Can you go on?

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