SOLUTION: Exponential and Logarithmic Functions (1)Let f(x) = 2^x , g(x) = (1/8)^x, and h(x) = log sub 2(x). Find each of the following: f(3) f(-2) f(1/2) g(2) g(-1) g(1

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Exponential and Logarithmic Functions (1)Let f(x) = 2^x , g(x) = (1/8)^x, and h(x) = log sub 2(x). Find each of the following: f(3) f(-2) f(1/2) g(2) g(-1) g(1      Log On


   

Question 61834: Exponential and Logarithmic Functions
(1)Let f(x) = 2^x , g(x) = (1/8)^x, and h(x) = log sub 2(x). Find each of the following:
f(3)
f(-2)
f(1/2)
g(2)
g(-1)
g(1/3)
h(2)
h(1/2)

(2) Solve each of the following equations for the given variable
(a) 2^a = 16
(b) 3^z = 1/9
(c) 9^n = 3
(d) (1/5)^x = 25
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Exponential and Logarithmic Functions
(1)Let f(x) = 2^x , g(x) = (1/8)^x, and h(x) = log sub 2(x). Find each of the following:
f%283%29=2%5E3
highlight%28f%283%29=8%29
:
f%28-2%29=2%5E%28-2%29
f%28-2%29=1%2F2%5E2
highlight%28f%28-2%29=1%2F4%29
:
f%281%2F2%29=2%5E%281%2F2%29
highlight%28f%281%2F2%29=sqrt%282%29%29
:
g%282%29=%281%2F8%29%5E2
highlight%28g%282%29=1%2F64%29
:
g%28-1%29=%281%2F8%29%5E%28-1%29
highlight%28g%28-1%29=8%29
:
g%281%2F3%29=%281%2F8%29%5E%281%2F3%29
g%281%2F3%29=%281%2F2%5E3%29%5E%281%2F3%29
g%281%2F3%29=1%2F2%5E3%2F3
highlight%28g%281%2F3%29=1%2F2%29
:
h%282%29=log2%282%29
highlight%28h%282%29=1%29
:
h%281%2F2%29=log2%281%2F2%29
highlight%28h%281%2F2%29=-1%29
:
(2) Solve each of the following equations for the given variable
(a) 2%5Ea=16
2%5Ea=2%5E4
highlight%28a=4%29
If you can use a calculator and can't figure this out:
ln%282%5Ea%29=ln%2816%29
aln%282%29=ln%2816%29
aln%282%29%2Fln%282%29=ln%2816%29%2Fln%282%29
a=4 <---This can be done for any that you can't solve mentally as long as you have a log capable calculator.
:
(b) 3%5Ez=1%2F9
3%5Ez=9%5E%28-1%29
3%5Ez=%283%5E2%29%5E%28-1%29
3%5Ez=3%5E%28-2%29
highlight%28z=-2%29
:
(c) 9%5En+=+3
3%5E%282n%29=3%5E1
2n=1
2n%2F2=1%2F2
highlight%28n=1%2F2%29
:
(d) %281%2F5%29%5Ex=25
5%5E%28-1x%29=5%5E2
-x=2
highlight%28x=-2%29
:
Happy Calculating!!!