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Log Calculator

Evaluate log_b(x) using change-of-base with natural logs.

Clear formulas
Educational steps
Detail breakdown

log_b(x) = ln(x)/ln(b) with domain x>0, b>0, b≠1.

Limitation: Educational logarithms.

Jump to calculator · Sources & review

How to Use the Log Calculator

log_b(x) = ln(x)/ln(b) with domain x>0, b>0, b≠1.

1

Open the Log calculator and read field labels.

Match the mode

Educational logarithms.

What It Calculates

log_b(x) = ln(x)/ln(b) with domain x>0, b>0, b≠1.

Worked Examples

log₁₀(100)

Inputs

value:100
base:10

Result

2

10² = 100.

log₂(8)

Inputs

value:8
base:2

Result

3

2³ = 8.

ln via base e

Inputs

value:20
base:2.718281828

Result

≈2.996

Natural log approx.

Check your mode

Educational logarithms.

Frequently Asked Questions

Yes. Results keep the precision shown on the page unless the engine requires integers.

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Formulas

Standard definitions with assumptions noted below.

Formula

log_b​(​x​)​ ​=​ ln​(​x​)​​/​ln​(​b​)​

Scientific Background

Standard core definitions with assumptions stated on-page. Educational only—not professional certification.

Sources & review

Log Calculator documents the references behind its formulas and assumptions. Always treat results as educational estimates, not personalized professional advice.

Last reviewed

July 22, 2026

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