Prove that 1:loga ab + 1:logb ab=1

See below.

Step-by-step explanation:

1 : loga ab + 1 : logb ab

= 1 / (loga ab) + 1 / (loga ab / loga b) { change of log base)

= 1 / (loga ab) + loga b / (loga ab)

= (1 + loga b) / loga ab

= (1 + loga b) / (loga a + loga b) Now loga a = 1 so we have:

((1 + loga b) / (1 + loga b)

= 1.