3^x = 54, then 3^(x-2) =
A) 3.8
B) 4.5
C) 6.0
D) 7.3
E) 9.0
Please explain how you solved it...
2007-08-27 04:37:32 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
3^(x-2) = 3^x / 3² = 3^x / 9, so divide 54 by 9 to get 6, C.
2007-08-27 04:42:30 · answer #1 · answered by Philo 7 · 2⤊ 0⤋
54 = 2 * 3^3
so 2 * 3^1 = 6
2007-08-27 14:13:21 · answer #2 · answered by RobRoy 3 · 0⤊ 0⤋
Logarithms find exponents. Since your variable is an exponent, you should utilize logs.
1) Take log of each side of equal sign. log 3^x = log 54
2) Law of Logs says you move the exponent in front of the log. x(log3) = log 54.
3) Get x alone by dividing each side of equal sign by log 3.
4) x = 3.63
Then, to solve 3^(x - 2), substitute the value we found in step four above for x.
5) 3^(3.63 - 2) = 3^1.63 = 6
2007-08-27 11:45:48 · answer #3 · answered by dwalon2 4 · 0⤊ 0⤋
3^(x-2) = (3^x)/(3^2) = (3^x)/9 = 54/9 = 6
2007-08-27 12:09:47 · answer #4 · answered by Steiner 7 · 0⤊ 0⤋