Solving (log_2 x)−4=5 log_x 2

Aydin Jarvis

Aydin Jarvis

Answered question

2022-10-23

Solving ( log 2 x ) 4 = 5 log x 2
How do I solve the following equation?
( log 2 x ) 4 = 5 log x 2
I tried doing this:
log (x * X/32) = 4 2 and i got x^2 = 512
Also, how do I solve equations of the form log⋅log⋅=… ? logarithms

Answer & Explanation

Mohammad Cantrell

Mohammad Cantrell

Beginner2022-10-24Added 10 answers

Rewrite
5 log x 2 = 5 log 2 2 log 2 x ,
then rearrange the terms to get
( log 2 x ) 2 4 log 2 x 5 = 0
and make the substitution
y = log 2 x
and solve the quadratic
y 2 4 y 5 = 0.
Cory Russell

Cory Russell

Beginner2022-10-25Added 4 answers

HINT:
For use
log 2 x 4 = 5 log x 2
use log a b = log b log a = 1 log b a

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