Base 10
10^y
y = 2 → 100
Broadcast-clear math
Antilog Calculator
Turn a logarithm value and base into the original number using b^y. All calculations run privately in your browser with no sign-up.
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Antilogarithm tool
Enter the log result y and the base b. The antilog is b^y.
Result:
Antilog
...
Enter a logarithm value and a valid base to compute the antilog.
Using this calculator
- Type the logarithm value (y) from your problem.
- Enter the same base (b) used in the original log.
- Read the antilog in the result panel.
- Use Reset to return to base 10 and clear the fields.
What Is an Antilog?
An antilogarithm (antilog) is the inverse of a logarithm. If log_b(x) = y, then the antilog of y with base b is the number x = b^y.
Logarithms answer: "To what power must we raise b to get x?" Antilogs answer the reverse: "What is x when the exponent is y?" That inverse relationship is why antilogs appear in algebra, science, engineering, finance, and statistics whenever you convert log-scale results back to ordinary values.
The word antilogarithm means the same as antilog. On calculators, the common antilog uses base 10, while the natural antilog uses base e. This page keeps the calculator at the top so you can compute first, then read definitions, formulas, and examples below.
Real-world uses include recovering original measurements from log-scaled data, checking pH and decibel math, modeling exponential growth, and verifying homework where logarithm values are already given.
Definition
Antilog_b(y) = b^y, the value x such that log_b(x) = y.
Relationship with logs
Log and antilog undo each other when the base b stays the same.
Applications
Science labs, finance growth models, signal levels, and exam-style log problems.
Antilog Formula
General form (base b, logarithm value y): antilog_b(y) = b^y Base 10 (common antilog): Antilog(x) = 10^x Natural antilog (base e): antilog_e(y) = e^y (calculator key: exp or e^x) Base n (any valid base): antilog_n(y) = n^y where n > 0 and n ≠ 1 Example: log_10(1000) = 3 → antilog_10(3) = 10^3 = 1000
The base 10 form Antilog(x) = 10^x is the version most students see on scientific calculators. It assumes the logarithm value you have came from a common (base 10) log.
For natural logs, replace 10 with e. The mathematical meaning is unchanged: raise the base to the logarithm value.
Always use the same base that appeared in the original log equation. Mixing base 10 and base e is one of the most common antilog mistakes.
Use the calculator at the top of this page when you know y and b. It applies b^y instantly, including scientific notation inputs.
How to Calculate an Antilog
Follow these steps whether you work by hand, with a scientific calculator, or with the antilog tool at the top of this page.
Step 1
Identify the logarithm value
Read y from the equation log_b(x) = y or from a log-scale table. Example: if log_10(x) = 2.5, then y = 2.5.
Step 2
Determine the base
Use the same base as the original logarithm: 10 for common logs, e for natural logs, or another valid base n.
Step 3
Apply exponentiation
Compute b^y. For base 10, calculate 10^y. For base e, calculate e^y.
Step 4
Verify the result
Check that log_b(answer) returns y. Enter y and b in the calculator at the top to confirm quickly.
Common Antilog Bases
Most school and applied problems use one of these bases. Compare the formula before you calculate.
Base e
e^y
y = 1 → ≈ 2.718
Base 2
2^y
y = 4 → 16
Custom base n
n^y
n = 5, y = 2 → 25
Natural Antilog Calculator
The natural antilog uses Euler's number e ≈ 2.71828 as the base. When ln(x) = y, the natural antilog is x = e^y.
Scientific calculators label this function exp, e^x, or inverse ln. Engineering and calculus courses rely on it for continuous growth models.
To compute a natural antilog here, enter the logarithm value in the first field and type e (or 2.71828) in the base field, or use a decimal approximation your instructor allows.
ln(x) = y ⟺ x = e^y Natural antilog: exp(y) = e^yTry natural antilog (base e)
Antilog vs Logarithm
Logarithms and antilogs are inverse operations. A logarithm compresses a number into an exponent; an antilog restores the original value by exponentiation.
If you treat them as opposites, you avoid sign and base errors: whatever base you used for the log must appear in the antilog step.
| Topic | Logarithm | Antilog |
|---|---|---|
| Purpose | Find exponent y in b^y = x | Find x from given y using b^y |
| Typical notation | log_10, ln, log_b | 10^x, e^x, b^y |
| Calculator keys | log, ln | 10^x, exp, e^x |
| Common mistake | Using wrong base | Forgetting to match that base |
Antilog Table and Calculations
Before electronic calculators, students used printed antilog tables to look up b^y for base 10. You found the row for y and read the corresponding power of ten.
Today, tables are mainly teaching tools. They show why logarithms were invented to simplify multiplication: adding logs is equivalent to multiplying originals, and antilogs convert back.
For accuracy, prefer direct exponentiation or a trusted calculator. Round only at the end of multi-step science or finance problems unless your instructor specifies otherwise.
Historical table lookup
Locate y in the table body and read the mantissa, then apply the correct power of ten from the characteristic.
Scientific calculator
Use 10^x for common antilog or e^x for natural antilog after identifying the base.
Manual check
Raise b to y with exponent rules, then confirm log_b(result) = y.
Antilog Calculator
The antilog calculator at the top of this page is built for quick, accurate reversal of logarithms. Enter the logarithm value, choose your base, and read the antilog instantly.
It supports decimal inputs and scientific notation, validates the base (positive and not equal to 1), and shows the formula b^y alongside the numeric result so you can study and verify at the same time.
Use it for homework checks, exam practice, lab conversions, and engineering estimates. All arithmetic runs locally in your browser; nothing is sent to a server.
- Log value input: Type the exponent y from log_b(x) = y.
- Base selection: Use 10, e, 2, or any valid custom base.
- Instant output: Result updates as you type.
- Formula line: Displays b^y = result for transparency.
Common Antilog Mistakes
Catch these errors before they appear on tests or lab reports.
Using base 10 after a natural log problem
Fix: If the equation uses ln(x), antilog with e^y, not 10^y.
Forgetting that antilog means exponentiation
Fix: Write b^y explicitly before you touch a calculator.
Treating antilog as multiplication by b
Fix: Raise b to the power y. Example: antilog_10(3) = 1000, not 30.
Using base 1 or a negative base
Fix: Logarithms require a positive base that is not 1; antilogs follow the same rule.
Rounding too early in science problems
Fix: Keep extra digits through intermediate steps, round at the end.
Antilog Applications in Science
Antilogs turn log-scale measurements back into linear units you can interpret or graph.
Chemistry (pH)
pH is a log scale; antilog-style reasoning recovers hydrogen ion concentration from pH values.
Physics (decibels)
Sound intensity uses logs; reversing the scale requires powers of ten.
Engineering
Signal gain and loss calculations often move between log and linear domains.
Statistics and finance
Log-transformed data is exponentiated to report growth factors or forecasts.
Research modeling
Exponential curves fitted in log space convert back with antilogs for real-world rates.
Antilog Examples
Worked examples for base 10, natural antilog, custom bases, and scientific notation style inputs.
Base 10 example
Given log_10(x) = 3, find x.
antilog_10(3) = 10^3 = 1000
Antilog: 1000
Natural antilog example
Given ln(x) = 2, find x (base e).
e^2 ≈ 7.389056
Antilog: ≈ 7.389
Base 2 example
Given log_2(x) = 5, find x.
2^5 = 32
Antilog: 32
Fractional exponent
Given log_10(x) = 0.5, find x.
10^0.5 = √10 ≈ 3.162
Antilog: ≈ 3.162
Educational check
Verify: if x = 1000, then log_10(x) = 3.
Antilog_10(3) returns 1000, matching the original value.
Antilog: Consistent
FAQs About Antilogarithms
What is an antilogarithm?
An antilogarithm is the inverse of a logarithm. If log_b(x) = y, then antilog_b(y) = b^y = x.
What is the antilog formula for base 10?
For common logarithms, Antilog(x) = 10^x. The input x is the logarithm value on a base 10 scale.
How do I calculate an antilog?
Identify the logarithm value y and base b, then compute b^y. Verify by checking that log_b(result) = y.
What is the difference between antilog and logarithm?
Logarithms find exponents; antilogs apply exponents to recover the original number. They are inverse operations with the same base.
What is the natural antilog?
The natural antilog uses base e. If ln(x) = y, then x = e^y, often computed with the exp or e^x key.
Can I use scientific notation?
Yes. Enter values such as 1.2e-3 in the calculator fields when your problem uses scientific notation.
Why is my antilog undefined?
Bases must be positive and cannot equal 1. Extremely large exponents may also exceed practical display limits.
Where is the calculator on this page?
The antilog calculator stays at the top of the page in the hero section. Use the link Open the calculator or scroll to #calculator.