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Question

Solve the following equation:
log2(100x)+log2(10x)=14+log1x

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Solution

log2(100x)+log2(10x)=14+log1x(2+logx)2+(1+logx)2=14logx2(logx)2+6logx+5=14logx2(logx)2+6logx+5=14logx2(logx)2+71logx9=02(logx+9)(logx1)=0logx=92,1x=1092,10


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