Solve log_2 x=log_4(x+6) for x using the change of base formula. I already tried changing the base on both sides but that didn't work I know it must be in the form of a quadratic for a substitution to be made.

Layton Park

Layton Park

Answered question

2022-11-19

Solve log 2 x = log 4 ( x + 6 ) for x using the change of base formula.
I already tried changing the base on both sides but that didn't work I know it must be in the form of a quadratic for a substitution to be made.

Answer & Explanation

embutiridsl

embutiridsl

Beginner2022-11-20Added 26 answers

Hint:
From the change of basis formula you have log 2 x = 2 log 4 x = log 4 x 2
and
log 4 x 2 = log 4 ( x + 6 )
in R , iff
x 2 = ( x + 6 ) x + 6 > 0
Humberto Campbell

Humberto Campbell

Beginner2022-11-21Added 4 answers

Hint:
Assume:
log 2 x = y
then
x = 2 y = ( 4 1 / 2 ) y = 4 y / 2
which means
log 4 x = y / 2

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