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If (log)a3=2a n dlog b 8=3, then prove t...

If `(log)_a3=2a n dlog` b 8=3, then prove that `(log)_a b=(log)_3 4.`

Text Solution

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If ` log_(a) 3 = 2`
` rArr 3 = a^(2)`
` rArr a = sqrt3`
If ` log_(b) 8 = 3`
` rArr 8 = b^(3)`
` rArr b = 2`
So, ` log_(a) b = log_(sqrt3) 2 = x(let)`
` rArr 2 = (sqrt3)^(x)`
` rArr 4 = 3^(x)`
` rArr x = log_(3) 4`
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