We have, (2x)ln2 = (3y)ln3 ... (i) and 3logx = 2logy .... (ii) If x0,y0are the solution of these equations now , (2x0)log2 = (3y0)log3 Taking log on both sides, log 2 log (2x0) = log 3 log (3y0) ⇒
log2
log3
log (2x0) = log (3y0)
log2
log3
(log 2 + log x0) = log 3 + log y0 ... (iii) Taking log on both sides of Eq. (ii) log x0 log 3 = log y0 log 2 ⇒ log y0 =