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Question

Solve the following equation.
log5(4xx6)log5(2x2)=2

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Solution

log5(4x6)log5(2x2)=2log5(4x6)2x2)=24x62x2=54x6=5.2x104x5.2x+4=0

Therefore, 2x=1,4x=0,2

At x=0, given equation is not valid.
Therefore, 4x6<0.
Therefore, x=2 is the solution.

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