SOLUTION: log base 9 of 6=a, log base 27 of 18=b. Express b in terms of a.

Question 936231: log base 9 of 6=a, log base 27 of 18=b. Express b in terms of a.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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

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