Question 315266
: evaluate the exponential equation for three positive values of x, three negative values of x and at x=0; 
y = 2^x + 2
:
Three positive values for x
x=2
y = 2^2 + 2
y = 5
:
x=3
y = 2^3 + 2
y = 8 + 2
y = 10
:
x=4
y = 2^4 + 2
y = 16 + 2
y = 18
:
Three negative values for x
x=-2
y = 2^-2 + 2
y = .25 + 2
y = 2.25
:
x=-3
y = 2^-3 + 2
y = .125 + 2
y = 2.125
:
x=-4
y = 2^4 + 2
y = .0625 + 2
y = 2.0625
:
Chart
 x | y
------
-4 | 2.0625
-3 | 2.125
-2 | 2.25
 2 | 5
 3 | 10
 4 | 18

The graph
{{{ graph( 300, 200, -5, 5, -6, 20, 2^x+2) }}}
:
:
transform the second expression into the equivalent logarithmic equation;
 and evaluate the logarithmic equation for three values of x that are greater
 than 1, three values of x that are between 0 and 1, and at x=1.
 show your work. use the resulting ordered pairs to plot the graph of each function;
 
x = 4^y+2
4^y = x - 2
ln(4^y) = ln(x-2)
y*ln(4) = ln(x-2)
y = {{{ln(x-2)/ln(4)}}}
:
For 3 values greater than 1
x=3
y = {{{ln(3-2)/ln(4)}}}
y = {{{ln(1)/ln(4)}}}
y = {{{0/ln(4)}}}
y = 0
:
x=4
y = {{{ln(4-2)/ln(4)}}}
y = {{{ln(2)/ln(4)}}}
y = .5
:
x=6
y = {{{ln(6-2)/ln(4)}}}
y = {{{ln(4)/ln(4)}}}
y = 1
:
You cannot evaluate any values 2 or below (log of a negative number)
:
Chart
x | y
------
 3 | 0
 4 | .5
 6 | 1
The graph
{{{ graph( 300, 200, -2, 8, -2, 4, ln(x-2)/ln(4)) }}}