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Logarithm Base b of x

Calculate log base b of x using change of base: log(x) / log(b).

Author

Prof. Hans Muller

Math editorial contributor

German renewable energy engineer at TU Munich, pioneering grid-scale hydrogen storage solutions

Reviewed by

Dr. Samuel Okafor

Math content reviewer

Nigerian-Canadian data scientist with a PhD from the University of Toronto, building ML models for early cancer detection

Last updatedFebruary 22, 2026

PublishedFebruary 22, 2026

Table of Contents

  1. Reference values
  2. Calculator
  3. Reference table
  4. FAQs
  5. Methodology and review
  6. Related conversions

16 Value (x) Value (x); 5 Base (b) Base (b) =

1.722706 Logarithm Value

Representative value from the Logarithm Base b of x reference table.

Reference Values

Browse 76 reference values with individual detail pages for quick lookup.

Browse all reference values

Logarithm Base b of x

Calculate log base b of x using change of base: log(x) / log(b).

Calculated Result

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Reference Table

Use this complete table for quick lookup and internal linking to specific value pages.

Logarithm Base b of x Reference
Scenariolog_b(x)
0.125 Value (x) Value (x); 2 Base (b) Base (b)-3 Logarithm Value
0.125 Value (x) Value (x); 3 Base (b) Base (b)-1.892789 Logarithm Value
0.125 Value (x) Value (x); 5 Base (b) Base (b)-1.29203 Logarithm Value
0.125 Value (x) Value (x); 10 Base (b) Base (b)-0.90309 Logarithm Value
0.25 Value (x) Value (x); 2 Base (b) Base (b)-2 Logarithm Value
0.25 Value (x) Value (x); 3 Base (b) Base (b)-1.26186 Logarithm Value
0.25 Value (x) Value (x); 5 Base (b) Base (b)-0.861353 Logarithm Value
0.25 Value (x) Value (x); 10 Base (b) Base (b)-0.60206 Logarithm Value
0.5 Value (x) Value (x); 2 Base (b) Base (b)-1 Logarithm Value
0.5 Value (x) Value (x); 3 Base (b) Base (b)-0.63093 Logarithm Value
0.5 Value (x) Value (x); 5 Base (b) Base (b)-0.430677 Logarithm Value
0.5 Value (x) Value (x); 10 Base (b) Base (b)-0.30103 Logarithm Value
1 Value (x) Value (x); 2 Base (b) Base (b)0 Logarithm Value
1 Value (x) Value (x); 3 Base (b) Base (b)0 Logarithm Value
1 Value (x) Value (x); 5 Base (b) Base (b)0 Logarithm Value
1 Value (x) Value (x); 10 Base (b) Base (b)0 Logarithm Value
2 Value (x) Value (x); 2 Base (b) Base (b)1 Logarithm Value
2 Value (x) Value (x); 3 Base (b) Base (b)0.63093 Logarithm Value
2 Value (x) Value (x); 5 Base (b) Base (b)0.430677 Logarithm Value
2 Value (x) Value (x); 10 Base (b) Base (b)0.30103 Logarithm Value
4 Value (x) Value (x); 2 Base (b) Base (b)2 Logarithm Value
4 Value (x) Value (x); 3 Base (b) Base (b)1.26186 Logarithm Value
4 Value (x) Value (x); 5 Base (b) Base (b)0.861353 Logarithm Value
4 Value (x) Value (x); 10 Base (b) Base (b)0.60206 Logarithm Value
8 Value (x) Value (x); 2 Base (b) Base (b)3 Logarithm Value
8 Value (x) Value (x); 3 Base (b) Base (b)1.892789 Logarithm Value
8 Value (x) Value (x); 5 Base (b) Base (b)1.29203 Logarithm Value
8 Value (x) Value (x); 10 Base (b) Base (b)0.90309 Logarithm Value
9 Value (x) Value (x); 2 Base (b) Base (b)3.169925 Logarithm Value
9 Value (x) Value (x); 3 Base (b) Base (b)2 Logarithm Value
9 Value (x) Value (x); 5 Base (b) Base (b)1.365212 Logarithm Value
9 Value (x) Value (x); 10 Base (b) Base (b)0.954243 Logarithm Value
10 Value (x) Value (x); 2 Base (b) Base (b)3.321928 Logarithm Value
10 Value (x) Value (x); 3 Base (b) Base (b)2.095903 Logarithm Value
10 Value (x) Value (x); 5 Base (b) Base (b)1.430677 Logarithm Value
10 Value (x) Value (x); 10 Base (b) Base (b)1 Logarithm Value
16 Value (x) Value (x); 2 Base (b) Base (b)4 Logarithm Value
16 Value (x) Value (x); 3 Base (b) Base (b)2.523719 Logarithm Value
16 Value (x) Value (x); 5 Base (b) Base (b)1.722706 Logarithm Value
16 Value (x) Value (x); 10 Base (b) Base (b)1.20412 Logarithm Value
25 Value (x) Value (x); 2 Base (b) Base (b)4.643856 Logarithm Value
25 Value (x) Value (x); 3 Base (b) Base (b)2.929947 Logarithm Value
25 Value (x) Value (x); 5 Base (b) Base (b)2 Logarithm Value
25 Value (x) Value (x); 10 Base (b) Base (b)1.39794 Logarithm Value
27 Value (x) Value (x); 2 Base (b) Base (b)4.754888 Logarithm Value
27 Value (x) Value (x); 3 Base (b) Base (b)3 Logarithm Value
27 Value (x) Value (x); 5 Base (b) Base (b)2.047819 Logarithm Value
27 Value (x) Value (x); 10 Base (b) Base (b)1.431364 Logarithm Value
32 Value (x) Value (x); 2 Base (b) Base (b)5 Logarithm Value
32 Value (x) Value (x); 3 Base (b) Base (b)3.154649 Logarithm Value
32 Value (x) Value (x); 5 Base (b) Base (b)2.153383 Logarithm Value
32 Value (x) Value (x); 10 Base (b) Base (b)1.50515 Logarithm Value
64 Value (x) Value (x); 2 Base (b) Base (b)6 Logarithm Value
64 Value (x) Value (x); 3 Base (b) Base (b)3.785579 Logarithm Value
64 Value (x) Value (x); 5 Base (b) Base (b)2.584059 Logarithm Value
64 Value (x) Value (x); 10 Base (b) Base (b)1.80618 Logarithm Value
81 Value (x) Value (x); 2 Base (b) Base (b)6.33985 Logarithm Value
81 Value (x) Value (x); 3 Base (b) Base (b)4 Logarithm Value
81 Value (x) Value (x); 5 Base (b) Base (b)2.730425 Logarithm Value
81 Value (x) Value (x); 10 Base (b) Base (b)1.908485 Logarithm Value
100 Value (x) Value (x); 2 Base (b) Base (b)6.643856 Logarithm Value
100 Value (x) Value (x); 3 Base (b) Base (b)4.191807 Logarithm Value
100 Value (x) Value (x); 5 Base (b) Base (b)2.861353 Logarithm Value
100 Value (x) Value (x); 10 Base (b) Base (b)2 Logarithm Value
125 Value (x) Value (x); 2 Base (b) Base (b)6.965784 Logarithm Value
125 Value (x) Value (x); 3 Base (b) Base (b)4.394921 Logarithm Value
125 Value (x) Value (x); 5 Base (b) Base (b)3 Logarithm Value
125 Value (x) Value (x); 10 Base (b) Base (b)2.09691 Logarithm Value
256 Value (x) Value (x); 2 Base (b) Base (b)8 Logarithm Value
256 Value (x) Value (x); 3 Base (b) Base (b)5.047438 Logarithm Value
256 Value (x) Value (x); 5 Base (b) Base (b)3.445412 Logarithm Value
256 Value (x) Value (x); 10 Base (b) Base (b)2.40824 Logarithm Value
1,000 Value (x) Value (x); 2 Base (b) Base (b)9.965784 Logarithm Value
1,000 Value (x) Value (x); 3 Base (b) Base (b)6.28771 Logarithm Value
1,000 Value (x) Value (x); 5 Base (b) Base (b)4.29203 Logarithm Value
1,000 Value (x) Value (x); 10 Base (b) Base (b)3 Logarithm Value

Frequently Asked Questions

Common questions about Logarithm Base b of x, formulas, and typical use cases.

What does the Logarithm Base b of x calculator do?

It helps with solving exponential equations and converting between logarithm bases.

What formula does the Logarithm Base b of x calculator use?

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

What inputs are valid?

x must be positive and base b must be positive and not equal to 1.

When would I use this?

solving exponential equations and converting between logarithm bases

Methodology and Review

This page combines a live calculator, precomputed reference values, and FAQ content from the same conversion definition to reduce mismatch between calculator output and lookup tables.

Editorial metadata (author, reviewer, and update date) is rendered on the page and in structured data. See our editorial policy, review process, and corrections policy.

For compliance-sensitive work, verify final values against project requirements, governing standards, and manufacturer documentation.