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How Do You Change Log Numbers On A Calculator?

Published Aug 29, 2025 4 min read
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On most scientific and graphing calculators, you change the logarithm's base using the Change of Base Formula. The formula states:

logb(x)=loga(x)loga(b)l o g sub b of x equals the fraction with numerator l o g sub a of x and denominator l o g sub a of b end-fraction

𝑙𝑜𝑔𝑏(𝑥)=𝑙𝑜𝑔𝑎(𝑥)𝑙𝑜𝑔𝑎(𝑏)

Where:

  • **logb(x)l o g sub b of x

    𝑙𝑜𝑔𝑏(𝑥)** is the original logarithm you need to solve.

  • **aa

    𝑎** is the new base you're converting to. On most calculators, this will be base 10 (the log button) or base e (the ln button).

  • **bb

    𝑏** is the original base of the logarithm.

  • **xx

    𝑥** is the number (or argument) you're taking the logarithm of.

Some modern graphing calculators, like the TI-84 Plus, have a built-in logBASE function that allows you to enter any base directly, bypassing the formula.

How to use the Change of Base Formula

The Change of Base Formula is a powerful tool because most calculators only have dedicated buttons for base-10 logarithms (labeled log) and natural logarithms (labeled ln). The formula allows you to calculate a logarithm of any base by using these two buttons.

Example: Evaluate log5(100)l o g sub 5 of 100

𝑙𝑜𝑔5(100)

  1. Identify the values:

    • Original base (bb

      𝑏

      ) = 5

    • Number (xx

      𝑥

      ) = 100

    • New base (aa

      𝑎

      ) = 10 (for the log button)

  2. Set up the formula: Using the change of base formula, log5(100)=log(100)log(5)l o g sub 5 of 100 equals the fraction with numerator l o g of 100 and denominator l o g of 5 end-fraction

    𝑙𝑜𝑔5(100)=𝑙𝑜𝑔(100)𝑙𝑜𝑔(5)

    .

  3. Calculate on your calculator:

    • Press the log button, type 100, and press ).
    • Press the division key (/).
    • Press the log button, type 5, and press ).
    • The calculation will look like this: log(100) / log(5).

  4. Get the result: The answer is approximately 2.86135.

Using modern graphing calculator functions

Newer graphing calculators, such as the TI-84 Plus CE

, have a dedicated function that simplifies this process.

Example: Evaluate log5(100)l o g sub 5 of 100

𝑙𝑜𝑔5(100)

on a TI-84 Plus CE

  1. Press the MATH button.
  2. Scroll down to option A: logBASE( and press ENTER.
  3. A template with boxes will appear on your screen.
  4. Use the arrow keys to enter 5 in the small box for the base and 100 in the larger box for the number.
  5. Press ENTER to get the result.

Changing the log number from a value

"Changing the log number" usually refers to finding the original number from its logarithm, also known as finding the antilogarithm. The antilogarithm is the inverse of the logarithm and is calculated by raising the base to the power of the log value.

Example: Find the number whose log (base 10) is 2.86135.

  1. Use the inverse function: Since the base is 10, the inverse is 10x10 to the x-th power

    10𝑥

    .

  2. On most calculators, press 2nd followed by the log button to access the 10x10 to the x-th power

    10𝑥

    function.

  3. Type 2.86135 and press ENTER.

  4. The result will be approximately 726.6, which is the original number.

Explanation and context of logarithmic functions

What is a logarithm?

A logarithm answers the question: "What exponent do you need to raise a specific base to, in order to get another number?" For instance, in the expression log10(100)=2l o g sub 10 of 100 equals 2

𝑙𝑜𝑔10(100)=2

, the base is 10, the number is 100, and the logarithm is 2. This is because 102=10010 squared equals 100

102=100

.

The importance of the base

The base of the logarithm is crucial, as it defines the exponential scale being used.

  • Base-10 (Common Log): The log button on calculators. It's used extensively in fields like chemistry (pH scale), physics (decibels), and engineering because it's based on the decimal system.
  • Base-e (Natural Log): The ln button on calculators. This is used in calculus, physics, and financial modeling to describe processes involving continuous growth and decay, such as compound interest and radioactive decay.
  • Other bases: Base-2 logarithms are important in computer science and information theory.

The role of the Change of Base Formula

Historically, before graphing calculators with dedicated logBASE functions, the Change of Base Formula was the only way for students and professionals to calculate logarithms for any base using a standard calculator. Even with modern calculators, understanding the formula is critical for:

  • Solving more complex logarithmic equations algebraically.
  • Working with calculators that don't have the advanced logBASE function.
  • Reinforcing the underlying mathematical principles of logarithms.

Common pitfalls and tips

  • Parentheses are essential: When entering the Change of Base Formula, especially on simpler scientific calculators, be sure to enclose both the numerator and the denominator in parentheses. This prevents calculation errors.

  • Choose your base wisely: You can use either log (base 10) or ln (base e) in the Change of Base Formula. The result will be the same regardless of your choice, as long as you are consistent. For example, log5(100)=log(100)log(5)=ln(100)ln(5)l o g sub 5 of 100 equals the fraction with numerator l o g of 100 and denominator l o g of 5 end-fraction equals the fraction with numerator l n open paren 100 close paren and denominator l n open paren 5 close paren end-fraction

    𝑙𝑜𝑔5(100)=𝑙𝑜𝑔(100)𝑙𝑜𝑔(5)=𝑙𝑛(100)𝑙𝑛(5)

    .

  • Know your calculator: Become familiar with the specific calculator model. Some have special menu functions (MATH menu on a TI, OPTN menu on a Casio) for accessing advanced logarithmic functions.

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