Unlock Logarithm Quotient Rule

Simplify complex logarithms using the quotient rule: log(a/b) = log(a) - log(b).

Logarithm Quotient Rule Calculator

Number A (Numerator)

The value of 'a' in log(a/b).

Number B (Denominator)

The value of 'b' in log(a/b).

Base

The base of the logarithm (e.g., 10, e, 2).

Result:

Visualization

The Quotient Rule for Logarithms states:

log(/) = log() - log()

Applying this rule with your inputs:

Result ≈

Understanding Logarithm Quotient Rule

The logarithm quotient rule is a fundamental property of logarithms that simplifies the logarithm of a quotient into the difference of logarithms. Specifically, for any positive numbers a, b, and a base c (where c ≠ 1), the rule is expressed as:

log_c(a/b) = log_c(a) - log_c(b)

This rule is incredibly useful in simplifying logarithmic expressions and solving equations involving logarithms. For example, it allows you to break down complex logarithmic problems into simpler, manageable parts.

Use this calculator to quickly apply the quotient rule and explore the relationships between logarithms.

Example

Calculate log₁₀(100/10):

Using the quotient rule: log₁₀(100/10) = log₁₀(100) - log₁₀(10)
log₁₀(100) = 2 (since 10² = 100)
log₁₀(10) = 1 (since 10¹ = 10)
Therefore, log₁₀(100/10) = 2 - 1 = 1