Question

if log x base p=a & log x base q=b,prove that ,logx base p/q = ab/b-a

Answer 1

now
LHS=log (x base p/q)

=1/(log (p/q base x )

=1/{log(p base x)-log (q base x )}

=1/{1/log (x base p)- 1/log (x base q)}

=1/{1/a - 1/b}

=1/{(b-a)/ab}

=ab/(b-a)= RHS