How to Change Log Base in Calculator

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Reviewed by: David Chen, CFA • Updated: October 2023

Most standard calculators only feature buttons for common logarithms (base 10) and natural logarithms (base e). To solve logarithms with any other base, you must apply the Change of Base Formula. This tool simplifies that process for you instantly.

How to Change Log Base in Calculator

The number you want to find the log of.
The base of the original logarithm.
The button available on your calculator.
Result: 0.00

how to change log base in calculator Formula:

$$\log_b(x) = \frac{\log_k(x)}{\log_k(b)}$$

Source: Khan Academy – Change of Base Review

Variables:

  • x (Value): The argument of the logarithm. Must be greater than 0.
  • b (Original Base): The base you are starting with. Must be positive and not equal to 1.
  • k (Target Base): The base your calculator supports (usually 10 or e).

What is how to change log base in calculator?

Changing the log base is a mathematical technique used to evaluate logarithms when your calculating device lacks a specific base button. Since most physical and digital calculators only provide “log” (base 10) and “ln” (base e), this formula bridges the gap.

By dividing the log of the value by the log of the base (both using the same new base), you arrive at the correct exponent for any arbitrary base. This is fundamental for solving exponential equations in computer science (base 2) and finance.

How to Calculate (Example):

To find $\log_2(8)$ using a common calculator (base 10):

  1. Identify the value ($x = 8$) and the original base ($b = 2$).
  2. Calculate $\log_{10}(8) \approx 0.903$.
  3. Calculate $\log_{10}(2) \approx 0.301$.
  4. Divide: $0.903 / 0.301 = 3$.

Related Calculators:

Frequently Asked Questions (FAQ):

Can the log base be negative? No, the base of a logarithm must always be a positive number and cannot be 1.

What is the “log” button on a calculator? On most standard calculators, the “log” button refers to the common logarithm (base 10).

What is the “ln” button? The “ln” button represents the natural logarithm, which uses the mathematical constant e ($\approx 2.718$).

Why can’t the base be 1? Because 1 raised to any power is always 1, making it impossible to reach any value other than 1 via exponentiation.

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