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How to Put Log Base in Calculator

Reviewed by Calculator Editorial Team

Calculating logarithms with different bases is a common mathematical task. This guide explains how to properly input log base in a calculator and understand the results.

How to Use the Log Base Calculator

Using a calculator to compute logarithms with different bases follows these steps:

  1. Enter the number you want to calculate the logarithm of in the "Number" field.
  2. Select the base you want to use from the "Base" dropdown menu.
  3. Click the "Calculate" button to get the result.
  4. Review the result and explanation provided.

The calculator will show you the logarithm value and explain how it was calculated.

Logarithm Formula

The logarithm of a number y with base b is the exponent x that satisfies the equation:

bx = y

Or written as: logb(y) = x

Common logarithm bases include:

  • Base 10 (common logarithm)
  • Base e (natural logarithm)
  • Base 2 (binary logarithm)

Worked Examples

Example 1: Base 10 Logarithm

Calculate log10(1000):

103 = 1000

Therefore, log10(1000) = 3

Example 2: Base 2 Logarithm

Calculate log2(16):

24 = 16

Therefore, log2(16) = 4

Example 3: Natural Logarithm

Calculate ln(e2):

e2 = e2

Therefore, ln(e2) = 2

FAQ

What is the difference between log and ln?

log typically refers to base 10 logarithms, while ln refers to natural logarithms (base e).

Can I calculate logarithms with any base?

Yes, you can calculate logarithms with any positive base except 1. The formula logb(y) = ln(y)/ln(b) allows for any base calculation.

What happens if I try to calculate log1(y)?

Logarithms with base 1 are undefined because 1x = 1 for any x, which doesn't satisfy the logarithm definition.