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There exists a positive number k such th...

There exists a positive number k such that ` log_2x+ log_4x+ log_8x= log_kx`, for all positive real no x. If k=`a^(1/b)` where (a,b) `epsilon` N, the smallest possible value of (a+b)= (C) 12 A) 75 (B) 65 (D) 63_

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`log_2^x+log_4^x+log_8^x`
`logx/log2+logx/log4+logx/log8`
`logx/log2+logx/(2log2)+logx/(3log2)`
`logx/log2(1+1/2+1/3)`
`logx/log2*11/6`
`logx/log2^(6/11)`
`log_(6/11)^x=log_k^x`
`k=2^(6/11)`
...
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