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Question

If log2x+log2x+log4(x2)+log8(x3)+log16(x4)=40 then x is equal to

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Solution

log2x+log2x+log4x2+log8x3+log16x4=40
log2xlog22+log2x+log2x2log24+log2x3log28+log2x4log216=40
log2xlog221/2+log2x+log2x2log222+log2x3log223+log2x4log224=40
2log2x+log2x+12log2x2+13log2x3+14log2x4=40
22log2x+22log2x+22log2x+33log2x+44log2x=40
log2x+log2x+log2x+log2x+log2x=40
5log2x=40
log2x=8
2log2x=28
x=28
x=256

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