Question

Describe the process of solving an exponential equation. Give two examples.

Answer 1

THE PROCESS FOR SOLVING EXPONENTIAL EQUATION:

Exponential equations are equations in which variables occur as exponents.

For example, exponential equations are in the form a^x=b^y

To solve exponential equations with same base, use the property of equality of exponential functions .

If b is a positive number other than 1 , then b^x=b^y if and only if x=y . In other words, if the bases are the same, then the exponents must be equal.   

Example 1:

Solve the equation 4^2x-1=64

Note that the bases are not the same. But we can rewrite 64 as a base of 4 .

We know that, 4³=64

Rewrite 64 as 4³ so each side has the same base.

4^2x-1=4³

By the property of equality of exponential functions, if the bases are the same, then the exponents must be equal.

2x−1=3

Add 1 to each side.

2x−1+1=3+1

2x=4

Divide each side by 2 .

2x/2=4/2

x=2

EXAMPLE 2:-

Again, there really isn’t much to do here other than set the exponents equal since the base is the same in both exponentials.

                                 

In this case we get two solutions to the equation. That is perfectly acceptable so don’t worry about it when it happens.