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If (log)a3=2and (log)b8=3, then prove th...

If `(log)_a3=2`and` (log)_b8=3`, then prove that `(log)_a b=(log)_3 4.`

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`log_a^3=2-(1)`
`log_b^8=3-(2)`
`(log_e^3/log_e^a)=2-(a)`
`(log_e^8/log_e^b)=3-(b)`
Dividing equation B from equation A
`(log_e^3*log_e^b)/(log_e^a*log_e^8)=2/3`
`(log_e^b)/(log_e^a)=2/3*(log_e^8/log_e^3)`
`log_a^b=2/3log_3^8`
...
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