Solve for x:
5^x - 5^(x-2) = 120(sqrt 5)
2007-02-11 16:11:39 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
How did you get 24/25 ?
2007-02-11 16:46:44 · update #1
Use exponent rules to rewrite the left-hand side:
5^x - 5^(x-2) = 120(sqrt 5)
5^x - (5^x)/25 = 120(sqrt 5)
(24/25)(5^x) = 120(sqrt 5)
5^x = (25/24)120(sqrt 5)
5^x = 25(120/24)sqrt(5)
5^x = 25(5)sqrt(5)
5^x = (5^2)(5^1)(5^.5)
5^x = 5^(2+1+.5)
5^x = 5^3.5
x=3.5
2007-02-11 16:22:24 · answer #1 · answered by Doc B 6 · 0⤊ 0⤋
5^x -5^(x-2) =120sqrt5 5^x -5^(-2) *5^x = 120 sqrt5
5^-2 =1/25 If yyou put 5^x=z you get z(1-1/25) =120 sqrt5
z= 120*25/24 *sqrt5 = 5 *25 *sqrt5= 5^x Now take log in base 5
log 5 +2log5 +log5/2 =xlog 5 but log 5 in base 5 is 1
So x=7/2
2007-02-12 07:00:01 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋