If 5^x – 5^(x - 3) = (124)(5^y), what is y in terms of x?
A. x
B. x - 6
C. x - 3
D. 2x + 3
E. 2x + 6
2007-05-08 18:14:49 · 4 answers · asked by msportobello 1 in Science & Mathematics ➔ Mathematics
5^x – 5^(x - 3) = (124)(5^y)
5^(x-3)[5^3 - 1] = (124)(5^y)
5^(x-3)* 124 = 124*5^y
5^(x-3)=5^y
x-3=y
y=x-3
C
2007-05-08 18:23:49 · answer #1 · answered by gudspeling 7 · 1⤊ 0⤋
The trick is the following:
5^(x-3)=5^x/125.
5^x-5^x/125= 124/125*5^x
So what we get is 124/125*5^x=124*5^y
5^x=125*5^y
Now we take the log base 5 of both sides, and we get
x=3+y
y=x-3
2007-05-08 18:24:19 · answer #2 · answered by singlepun 3 · 1⤊ 0⤋
factor:
( 5 ^ (x-3) ) ( ( 5^3 - 1 ) = 124 (5^y)
see that 5^(3) = 125
( 5 ^ (x-3) ) 124 = 124 (5^y)
5 ^ (x-3) ) = (5^y)
take log (base 5) of both sides:
x - 3 = y
2007-05-08 18:31:43 · answer #3 · answered by Hk 4 · 0⤊ 0⤋
5^(x-3)[125-1]=1245^y
so, y=x-3 or C
2007-05-08 18:27:23 · answer #4 · answered by bruinfan 7 · 0⤊ 0⤋