Prove that (log_a X)/(log_ab X) = 1 + log_a b

prove that (log_a X)/(log_ab X) = 1 + log_a b
thank you!
im fallin a bit behind in math and i dont understand change of base?

Use change of base formula,
(log_a X)/(log_ab X)
= (lnX/lna)/(lnX/lnab)
= lnab/lna
= 1 + lnb/lna
= 1 + log_a b

log_a (x)=ln x/ ln a--------------------1

log_ab (x)=ln x/ln(ab)----------------2

1 divided by 2,

log_a (x)/log_ab (x)=ln(ab)/ln(a)

=[ln a+ ln b]/ln a

=1+(ln b/ ln a)

=1+log_a (b)

Using the property, log_a (b)= ln b/ ln a

where ln=log base e