If a and b are positive integers and 9(3^a)=3^b, what is a in terms of b? The answer is b-2, but why?!
(^ = power/exponent)
I have wracked my brain and I cannot figure out why a in terms of b is b-2. If the 9 wasn't there, I know a would be equal to b... but having to multiply that left side by 9 is totally throwing me off. HELP!
2006-09-24 12:37:38 · 3 answers · asked by trying <3 2 in Education & Reference ➔ Homework Help
Look: 9 = 3^2.
So, 9(3^a) = 3^2(3^a) = 3^(a+2) = 3^b.
So, a + 2 = b, or a = b-2.
Hope that helps!
2006-09-24 12:44:07 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋
9(3^a) = 3^b
==> 3^a = (3^b)/9
3^a = (3^b)/(3^2)
3^a= (3^b)(3^-2)
3^a= 3^(b-2)
==> a=b-2
2006-09-24 19:55:45 · answer #2 · answered by help563 2 · 0⤊ 0⤋
9(3^a)=3^b
take the ln (natural log) of both sides:
ln(9) + a*ln(3) = b*ln(3)
a = (b*ln(3) - ln(9)) / ln(3)
2006-09-24 19:40:23 · answer #3 · answered by Will 6 · 0⤊ 0⤋