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The value of loga(x)/log(ab)x-logab...

The value of `log_a(x)/log_(ab)x-log_ab`

Text Solution

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We know, `log_mn = logn/logm`
`:. log_a(x)/log_(ab)x - log_ab = (logx/loga)/(logx/log(ab))-logb/loga`
`=log(ab)/(loga) - logb/loga`
`=1/(loga)(log(ab)-logb)`
As `logm - logn = log(m/n)`, our expression becomes,
` = 1/loga(log((ab)/b)`
`=loga/loga = 1`
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