Find the zero of the function y=2^(-2(x+5)) - √8
2007-05-23 13:08:56 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Set y=0:
0 = 2^(-2(x+5)) - √8
Add √8:
√8 = 2^(-2(x+5))
Take the log, base 2, of both sides:
log₂ (√8) = -2(x+5)
Use the laws of logarithms to simplify:
1/2 log₂ 8 = -2(x+5)
3/2 = -2(x+5)
Distribute:
3/2 = -2x-10
Add 10:
23/2 = -2x
Divide by -2:
x=-23/4
And we are done.
2007-05-23 13:17:04 · answer #1 · answered by Pascal 7 · 0⤊ 0⤋
-2(x+5) = log base 2 of sqrt(8) = 3/2
x + 5 = -3/4
x = -5 - 3/4 = -23/4
2007-05-23 20:22:14 · answer #2 · answered by jcsuperstar714 4 · 0⤊ 0⤋
-5.75
2^(-2(x+5)) - â8 = 0
2^(-2(x+5)) = â8 = 2^(3/2)
-2(x+5) = 3/2
x+5 = -3/4
x = -23/4 = -5.75
2007-05-23 20:15:27 · answer #3 · answered by Scott R 6 · 1⤊ 1⤋
y = 2^(-2x-10) - â8 = 0
2^(-2x-10) = 2^(3/2)
-2x - 10 = 3/2
-2x = 23/2
x = -23/4
2007-05-23 20:16:22 · answer #4 · answered by Philo 7 · 0⤊ 0⤋