Main content

### Course: Algebra (all content) > Unit 11

Lesson 25: Solving exponential equations with logarithms (Algebra 2 level)- Solving exponential equations using logarithms: base-10
- Solving exponential equations using logarithms
- Solve exponential equations using logarithms: base-10 and base-e
- Solving exponential equations using logarithms: base-2
- Solve exponential equations using logarithms: base-2 and other bases

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Solving exponential equations using logarithms: base-2

We can use logarithms to solve *any* exponential equation of the form a⋅bᶜˣ=d. For example, this is how you can solve 3⋅10²ˣ=7:

1. Divide by 3: 10²ˣ=7/3

2. Use the definition of logarithm: 2x=log(7/3)

3. Divide by 2: x=log(7/3)/2 Now you can use a calculator to find the solution of the equation as a rounded decimal number

. Created by Sal Khan.

1. Divide by 3: 10²ˣ=7/3

2. Use the definition of logarithm: 2x=log(7/3)

3. Divide by 2: x=log(7/3)/2 Now you can use a calculator to find the solution of the equation as a rounded decimal number

. Created by Sal Khan.

## Want to join the conversation?

No posts yet.