How to Change the Log Base on a Calculator

Reviewed by David Chen, CFA Financial Analysis & Mathematics Expert

Most calculators only have buttons for Log (base 10) and Ln (base e). Use this tool to calculate a logarithm with any base instantly using the change of base formula.

Change of Log Base

how to change the log base on a calculator Formula:

log_a(x) = log_b(x) / log_b(a)

Source: Wolfram MathWorld – Logarithm Rules | Khan Academy

Variables:

• x (Number): The value you want to find the logarithm of.
• b (Current Base): The base that your calculator or current expression uses (usually 10 or e).
• a (New Base): The target base you want to convert the expression into.

Related Calculators:

• Natural Logarithm (ln) Solver
• Antilogarithm Calculator
• Binary Log (Base 2) Converter
• Exponential Growth Calculator

What is how to change the log base on a calculator?

Logarithms are the inverse of exponentiation. However, most standard scientific calculators only provide two types of logarithms: the common logarithm (base 10, often labeled “log”) and the natural logarithm (base e, approximately 2.718, labeled “ln”).

If you need to find log₃(81), most handheld calculators won’t have a “base 3” button. To solve this, you must apply the Change of Base Formula, which allows you to rewrite any logarithm in terms of bases your calculator *does* support, like base 10 or base e.

How to Calculate how to change the log base on a calculator (Example):

Let’s say you want to calculate log₂(50) using a standard calculator (base 10).

1. Identify your values: x = 50, new base a = 2.
2. Choose a base your calculator has (usually base 10).
3. Apply the formula: log₂(50) = log₁₀(50) / log₁₀(2).
4. Calculate the parts: log₁₀(50) ≈ 1.69897 and log₁₀(2) ≈ 0.30103.
5. Divide: 1.69897 / 0.30103 = 5.6438.

Frequently Asked Questions (FAQ):

Why do I need to change the log base?

You need it because most computing devices only support base 10 (common) and base e (natural). It allows you to solve problems involving custom bases like base 2 (binary) or base 3.

Does it matter which base I use for the conversion?

No. Whether you use log₁₀ or ln (base e) to perform the division, the final result will be identical as long as you use the same base for both the numerator and the denominator.

What if the base is 1?

Logarithms cannot have a base of 1 because 1 raised to any power is always 1, making it impossible to reach other numbers. The base must be positive and not equal to 1.

Can the number (x) be negative?

In standard real-number mathematics, the argument of a logarithm (x) must be greater than zero. Negative numbers and zero do not have real-number logarithms.