If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

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.

Video transcript