Pre-calculus algebra logarithm question I don't understand how to solve this equation. Been struggling with it and don't know how to start: log_2 x=8+9log_x 2 Can someone please help me out?

Altenbraknz 2022-09-17 Answered
Pre-calculus algebra logarithm question
I don't understand how to solve this equation. Been struggling with it and don't know how to start:
log 2 x = 8 + 9 log x 2
Can someone please help me out?
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Answers (2)

lufi8c
Answered 2022-09-18 Author has 11 answers
log 2 x 8 9 log x 2 = 0
Using log x 2 = 1 log 2 x and setting u = log 2 x we get:
u 8 9 u u 2 8 u 9 = 0 ( u 9 ) ( u + 1 ) = 0
This gives log 2 x = 1 x = 1 2 or log 2 x = 9 x = 512

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imchasou
Answered 2022-09-19 Author has 2 answers
HINT:
Use
log a b = log b log a
to form a Quadratic Equation in log x

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