Exponential & Logarithm Worksheets

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There are four sets of logarithm & exponential worksheets:

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: bx = y

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

Logarithmic Form: logb(y) = x

  • logb 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 bx = y, the logarithmic form is logb(y) = x
    Example: 102 = 100, so log10(100) = 2

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

  3. Common Logarithmic Bases:
    In mathematics, common logarithms use base 10. So, logb(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.

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

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

Exponential & Logarithmic Worksheet

More Exponential & Logarithmic Worksheets

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

Exponential and Logarithmic Functions

More Printable Worksheets

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