Logarithms - How to Graph
Logarithms - How to Graph - Video
Example 1 Part 1
Example 1 Part 1:
The domain of logarithms can't be equal to negative numbers. When we want to graph, we have to pick positive numbers. The easiest numbers to pick are numbers that are associated with the base. Since our base is 2, we chose to pick 2 to the power of something. Since logarithms are a bit tougher to graph than a linear equation, we need a few more points to understand how we need to draw it.
We chose 20 as the first number then pick two numbers greater, 21 and 22 , and two numbers then pick two numbers smaller, 2-1 and 2-2.
Example 1 Part 2
Example 1 Part 2:
For every logb x = y, we can say by = x. So in our case we can say, 2y = x. We just chose our input values, x.
If we start with 2-2, we also know that 2-2 = 2y so y = -2.
Next we have 2-1, we also know that 2-1 = 2y so y = -1.
Next we have 20, we also know that 20 = 2y so y = 0.
Next we have 21, we also know that 21 = 2y so y = 1.
Last we have 22, we also know that 22 = 2y so y = 2.
Example 1 Part 3
Example 1 Part 3
Now let's simplify the rest of the XY table by using those powers.
2-2 equals 1/4.
Next, 2-1 equals 1/2.
Next, 20 equals 1.
Next, 21 equals 2.
Last, 22 equals 4.
Example 1 Part 4
Example 1 Part 4:
Now we converted each point in logarithm form
The point (1/4, -2) becomes -2 = log2 (1/4).
The point (1/2, -1) becomes -1 = log2 (1/2).
The point (1, 0) becomes 0 = log2 (1).
The point (2, 1) becomes 1 = log2 (2).
The point (4, 2) becomes 2 = log2 (4).
Finally we plotted the points and drew our line.
Example 1 Part 5
Example 1 Part 5:
The last part that we need to talk about is the asymptote and our range. Remember our domain is all positive numbers or x > 0. Now our asymptote is x = 0 because the graph never touches the y-axis which is also x = 0. It gets really really close, but it never actually touches it.
And our range is from negative infinity to positive infinity because it never stops going up nor down. Although it looks like it flattens out, it continues to increase ever so slightly.