# Solve Exponential Equations By Making Bases Same Worksheet

## 6 problems

To solve exponential equations by making the bases the same, rewrite each side of the equation to have the same base. Adjust the exponents so the bases match. Once the bases are identical, set the exponents equal to each other and solve for the variable. This method simplifies the process and ensures you find the correct solution by working with matching bases. The worksheet for solving exponential equations by making the bases the same provides practice problems for mastering this method.

Algebra 2
Exponential Functions

## How Will This Worksheet on "Solve Exponential Equations by Making Bases Same" Benefit Your Student's Learning?

• Converting bases transforms difficult exponential equations into simpler linear ones.
• This method helps students better understand and remember the rules of exponents.
• Simplifying exponential equations improves problem-solving skills.
• Knowing how to solve these equations is practical for real-life tasks like calculating interest and population growth.
• The process enhances logical thinking and careful analysis, improving overall math skills.
• The procedure improves logical questioning and careful evaluation, boosting normal math abilities.

## How to Solve Exponential Equations by Making Bases Same?

• Begin with an equation like $$a^x = b$$, where $$a$$ and $$b$$ are numbers with $$a \neq 1$$ and $$a > 0$$.
• Rewrite $$b$$ using the same base as $$a$$.
• Equate the exponents from both sides of the equation to solve for $$x$$.
• Substitute the solution back into the original equation to ensure it satisfies both sides.

These steps illustrate how to solve exponential equations by aligning their bases and equating their exponents.

## Solved Example

Q. Solve. Write your answer as an integer or a fraction in simplest form. $\newline$$9^x = 81$$\newline$$x =$ ______
Solution:
1. Rewrite as power of $9$: Rewrite $81$ as a power of $9$.$\newline$$81$ is the same as $9^2$.$\newline$So, $9^x = 9^2$.
2. Set exponents equal: Set the exponents equal to each other since the bases are the same. $x = 2$.

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