```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)=2^3}}}
{{{highlight(f(3)=8)}}}
:
{{{f(-2)=2^(-2)}}}
{{{f(-2)=1/2^2}}}
{{{highlight(f(-2)=1/4)}}}
:
{{{f(1/2)=2^(1/2)}}}
{{{highlight(f(1/2)=sqrt(2))}}}
:
{{{g(2)=(1/8)^2}}}
{{{highlight(g(2)=1/64)}}}
:
{{{g(-1)=(1/8)^(-1)}}}
{{{highlight(g(-1)=8)}}}
:
{{{g(1/3)=(1/8)^(1/3)}}}
{{{g(1/3)=(1/2^3)^(1/3)}}}
{{{g(1/3)=1/2^3/3}}}
{{{highlight(g(1/3)=1/2)}}}
:
{{{h(2)=log2(2)}}}
{{{highlight(h(2)=1)}}}
:
{{{h(1/2)=log2(1/2)}}}
{{{highlight(h(1/2)=-1)}}}
:

(2) Solve each of the following equations for the given variable
(a) {{{2^a=16}}}
{{{2^a=2^4}}}
{{{highlight(a=4)}}}
If you can use a calculator and can't figure this out:
{{{ln(2^a)=ln(16)}}}
{{{aln(2)=ln(16)}}}
{{{aln(2)/ln(2)=ln(16)/ln(2)}}}
{{{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^z=1/9}}}
{{{3^z=9^(-1)}}}
{{{3^z=(3^2)^(-1)}}}
{{{3^z=3^(-2)}}}
{{{highlight(z=-2)}}}
:
(c) {{{9^n = 3}}}
{{{3^(2n)=3^1}}}
{{{2n=1}}}
{{{2n/2=1/2}}}
{{{highlight(n=1/2)}}}
:
(d) {{{(1/5)^x=25}}}
{{{5^(-1x)=5^2}}}
{{{-x=2}}}
{{{highlight(x=-2)}}}
:
Happy Calculating!!!
```