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To draw the graph of a logarithmic function, we can follow a three-step process.
Let's do it!
Looking at the given functions, we can see that we have a common logarithm and natural logarithm. Recall that the base of the common logarithm is 10, and the natural logarithm has the number e as its base. With this in mind, let's highlight the base of each function. ccc f(x)=log_2x & ⇔ & f(x)=log_()darkorange2x f(x)=log x & ⇔ & f(x)=log_(10) x f(x)=ln x & ⇔ & f(x)=log_e x
Using the base b we can identify three points on the graph of a logarithmic function. ( 1b, - 1 ), (1,0), and (b,1) Since we know the bases, we can immediately determine these points.
| Function | Points |
|---|---|
| f(x)=log_()darkorange2x | ( 12, - 1 ), (1,0), and (2,1) |
| f(x)=log_(10) x | ( 1 10, - 1 ), (1,0), and ( 10,1) |
| f(x)=log_e x | ( 1 e, - 1 ), (1,0), and ( e,1) |
Finally, we will plot the points and connect them with a smooth curve.
