Exponential Equations

An exponential equation is an equation in which the variable appears in the exponent. The general form of an exponential equation is:

a^x = b

Where a is the base, x is the exponent, and b is a constant.

Solving Exponential Equations

To solve exponential equations, you can use the following methods:

1. Using the Same Base: If both sides of the equation have the same base, you can set the exponents equal to each other and solve for the variable.
2. Using Logarithms: If the base of the exponential equation is different from 1, you can use logarithms to solve for the variable. The general form of using logarithms is:

log_a(b) = x

Where a is the base of the logarithm, b is the constant, and x is the exponent.

Example

Let's solve the exponential equation 2^x = 8:

Using the Same Base method:

2^x = 2

x = 3

Using Logarithms method:

log₂(8) = x

x = 3

Study Guide

To study exponential equations, make sure to:

• Understand the basic concepts of exponents and bases.
• Practice solving exponential equations using the same base and logarithms.
• Review properties of logarithms and their applications in solving exponential equations.
• Work on various examples to strengthen your understanding of exponential equations.

Remember to always check your solutions by substituting them back into the original equation to ensure they are correct.

Now you are ready to tackle exponential equations with confidence!