No calculators I know of can do base 4 logarithms so don't feel bad that you couldn't figure how to use your calculator. The base 4 logarithms can be calculated "by hand" if the argument, x+2, turns out to be a power of 4. So we just have to pick x's so that x+2 works out to be a power of 4.
What are some powers of 4 and how do we figure out an x value that makes x+2 equal to those powers of 4?- Pick an integer (... -3, -2, -1, 0, 1, 2, 3, ...)
- Raise 4 to that power.
- Set that power of 4 equal to x+2.
- Solve for x (i.e. subtract 2 from each side).
- Keep track of which x goes with which integer exponent. The integer value will be the base 4 logarithm.
- Repeat this process until you have all the x's you need.
Here's some examples:
n 4 to the n power Equation to find x x y = log4(x+2)
(same as n)
0 1 x+2 = 1 -1 0
1 4 x+2 = 4 2 1
-1 1/4 x+2 = 1/4 -1.25 -1
2 16 x+2 = 16 14 2
-2 1/16 x+2 = 1/6 -1.9375 -2
You need one more x which works out between -1 and -2. I'll leave it up to you to find it.
With these pairs of x and y values (the last two columns) you have ordered pairs which you can plot on a graph. The "connect the dots" with as smooth a curve as possible.
As for the asymptote, logarithmic equations have vertical asymptotes for x values that make the argument of any logarithm zero, if any. To find your asymptote set you argument to zero and solve:
x + 2 = 0
x = -2
So your graph will have a vertical asymptote at x = -2.