Exponential & Logarithm Worksheets

There are four sets of logarithm & exponential worksheets:

• Exponential & Logarithmic Forms
  
• Evaluate Logarithms
  
• Expand Logarithms
  
• Condense Logarithms
  

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 students learn how to convert between exponential and logarithmic forms.

How to convert between exponential & logarithmic form worksheets?

There are two sets of convert between exponential & logarithmic forms worksheets.

• Convert from exponential to logarithmic forms.
• Convert from logarithmic to exponential forms.

Here’s how you can convert between exponential and logarithmic forms:

Exponential Form: b^x = y

• b is the base.
  
• x is the exponent.
  
• y is the result or value.
  

Logarithmic Form: log_b(y) = x

• log_b denotes the logarithm with base b.
  
• x is the exponent to which b must be raised to get y.

Here are some common conversions:

1. From Exponential to Logarithmic:
   Given b^x = y, the logarithmic form is log_b(y) = x
   Example: 10² = 100, so log₁₀(100) = 2
   

2. From Logarithmic to Exponential:
   Given log_b(y) = x, so the exponential form is b^x = y
   Example: log₂(8)=3, so 2³ = 8

3. Common Logarithmic Bases:
   In mathematics, common logarithms use base 10. So, log_b(y) is usually written as log(y)
   Example: log(1000) = 3 because 10³ = 1000

4. Natural Logarithms:
   The natural logarithm uses base e, where e is Euler’s number, approximately equal to 2.71828. The natural logarithm is often written as ln(y).
   Example: ln(e)=1 because e¹ = 1

Remember that logarithms are used to solve equations where the exponent (or power) is unknown and needs to be determined. They are also used to express exponential growth or decay problems in terms of time or other variables. Logarithmic functions are the inverse of exponential functions.

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Convert between Exponential & Logarithmic forms Worksheets.

 

More Exponential & Logarithmic Worksheets

Printable
(Answers on the second page.)
Exponential to Logarithm Worksheet
Logarithm to Exponential Worksheet

Related Lessons & Worksheets

Exponential and Logarithmic Functions
More Printable Worksheets

Have a look at this video if you need to review how to convert between exponential and logarithmic forms.

• Writing Logarithmic Equations In Exponential Form

Check out our most popular games!

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.