Quick Calculators

Logarithm Calculator (Any Base) | Solve Log Equations Easily

Logarithm Evaluator (Any Base)

High School Logarithm Evaluator

Calculate y = logb(x) for any base and visualize the curve.

Must be > 0 and ≠ 1

log

Must be > 0

= ?

Result

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Exponential Form

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Calculation Steps

Waiting for input…

Logarithm Evaluator Graph

Log Curve
Point (x, y)

Understanding Logarithms

A logarithm answers the question: “To what power must we raise a specific base to get a certain number?” In mathematical terms, if by = x, then logb(x) = y.

For example, because 23 = 8, we say that log2(8) = 3. The base is 2, the argument is 8, and the answer is 3.

Why use a Logarithm Evaluator?

While many calculators have a standard “log” button (base 10) and “ln” button (base e), they often lack a button for arbitrary bases like base 2 or base 5. This tool solves that problem instantly using the Change of Base Formula:

logb(x) = ln(x) / ln(b)

This formula allows us to calculate any logarithm using natural logarithms.

Key Properties

  • Product Rule: log(ab) = log(a) + log(b)
  • Quotient Rule: log(a/b) = log(a) – log(b)
  • Power Rule: log(an) = n · log(a)
  • Identity: logb(b) = 1 and logb(1) = 0

FAQ

Is this Logarithm Evaluator free?

Yes, this tool is free for all students and requires no downloads.

Why can’t the base be 1?

Because 1 raised to any power is still 1 (1y = 1). You cannot get any other number like 2 or 5 from base 1, so the logarithm is undefined.

Why can’t I use negative numbers?

Logarithms are undefined for negative numbers and zero because a positive base raised to any power always results in a positive number.

Can the Logarithm Evaluator handle decimals?

Yes! You can input decimal bases (like 0.5) and decimal arguments.

MIDDLE SCHOOL