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[Solved] Solving the logarithm equation

 
Logorithm
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June 15, 2021 2:39 pm
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Staff 
(@armor)
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Solve the equation system 

log_{2}x+log_{y}8=2,

log_{y}2+log_{8}x^2=1.

 

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June 15, 2021 2:39 pm
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

The system is equivalent to 

\small log_{2}x+\frac{3}{log_{2}y}=2      (i)

\small \frac{1}{log_{2}y}+\frac{2log_{2}x}{3}=1   (ii)

\small (ii)*3-(i)=log_{2}x=1\Rightarrow x=2.

Substitute it into (i):y=8.

We can easily verify x=2, y=8 is a solution of the original system.

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