Express as a single logarithm 40 log5 5x log540x6log5 40Solu

Express as a single logarithm. 40 log5 5x +log5(40x^6)-log5 40

log5 5x +log5(40x^6)-log5 40

Use following log formulas: logx +logy -logz = log(x*y/z)

a*logx = log(x^a)

So, log5 5x +log5(40x^6)-log5 40 = log5(x^5/2) + log5(40x^6) - log5(40)

= log5[( x^5/2*40x^6)/40]

= log5[x^(5/2)*x^6]

= log5[x^17/2]

= 17/2*logx