Question

How can logarithms be graphed with different bases?

Answer 1

Since logs and exponents are inverse functions, You can get the table for the exponential form and then switch the x and y values.
Ex. log base 2 x, get values for 2^x, then switch x & y

Answer 2

The steps for graphing the logarithmic functions with different bases are shown below.

Explanation:

Let the logarithmic function is defined as

`y=\log_ax`

where, x and y are variables, a is the base of logarithmic function.

The steps for graphing the logarithmic functions with different bases are:

1. Using the change base formula, rewrite the given function.

`y=(\log x)/(\log a)`, where,
`\log a\\eq 0\Rightarrow a\\eq 1`.

2. Find the y values for different values of x.

3. Create the table of values.

4. Plot the ordered pairs of table in the coordinate plane.

5. Joint the points by a free hand curve.