Question 936231
log(9,6) = a
log(27,18) = b
you want to express b in terms of a.


log(9,6) = a if and only if 9^a = 6
log(27,18) = b if and only if 27^b = 18


since 9 = 3^2, then 9^a can be expressed as (3^2)^a which becomes 3^(2a) and you get:


9^a = 6 becomes 3^(2a) = 6


since 27 = 3^3, then 27^b can be expressed as (3^3)^b which becomes 3^(3b) and you get:


27^b = 18 becomes 3^(3b) = 18


if you divide both sides of this equation by 3, you will get:


3^(3b) / 3 = 6


simplify to get:


3^(3b-1) = 6


you now have:


3^(2a) = 6 and 3^(3b-1) = 6


this can only be true if 2a = 3b-1


solve for b and you get b = (2a+1) / 3