Product of logartithms equation. Please help me whilst I do a few simple school tasks. I found this one, which is unbreakable for me. I will appreciate any help. log_2(x)=4/(log_2 x-3) I moved only with the fact that 4=log_2 16. I have no idea what to do next.

Josiah Owens

Josiah Owens

Answered question

2022-10-30

Product of logartithms equation.
Please help me whilst I do a few simple school tasks. I found this one, which is unbreakable for me. I will appreciate any help.
log 2 x = 4 log 2 x 3
I moved only with the fact that 4 = log 2 16. I have no idea what to do next.

Answer & Explanation

canhaulatlt

canhaulatlt

Beginner2022-10-31Added 17 answers

As far as I know, this doesn't have an elementary solution. The best I can get using numerical methods is x 5.94051. Was this an exercise in numerical methods?
If you meant log 2 x 3, then it can be solved the following way:
log 2 x ( log 2 x 3 ) = 4 ( log 2 x ) 2 3 log 2 x 4 = 0
Using a substitution u = log 2 x to get the above as
u 2 3 u 4 = 0
This has solutions u = 1 and u = 4. The first yields
log 2 x = 1 x = 1 2
and the second yields
log 2 x = 4 x = 16

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