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Question

Solve the following equation:
2log3(x2)+log3(x4)2=0

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Solution

2log3(x2)+log3(x4)2=0log3(x2)2+log3(x4)2=0[(x2)(x4)]2=1(x2)(x4)=±1x26x+8=±1

x26x+9=0 or x26x+7=0
Therefore, x=3 or x=6±82=3±2
at x=32, x2 is negative.
Therefore, x=3,3+2 are only solutions


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