Antilog Calculator
Calculate the inverse logarithm (bˣ)
- Enter the value (x): Input the exponent or logarithm value you want to find the antilog for. This is the power to which the base will be raised.
- Set the base: Choose the base for your calculation. The default is 10 (common antilog), but you can enter any positive number except 1. Use 2.71828 for natural antilog (base e).
- Calculate: Click the Calculate button to see the result. The calculator will compute base raised to the power of your input value.
Antilog, short for "antilogarithm," is the inverse operation of a logarithm. If you think of a logarithm as asking "what power do I raise this base to get a certain number?", then antilog answers the opposite question: "what number do I get when I raise this base to a certain power?"
The relationship between log and antilog is straightforward. If logb(x) = y, then antilogb(y) = x. In other words, applying log and then antilog (or vice versa) brings you back to your original number.
The most common bases you'll encounter are:
- Base 10: Called the common logarithm base, used in scientific notation and many engineering applications
- Base e (2.71828...): Called the natural logarithm base, fundamental in calculus, physics, and continuous growth calculations
- Base 2: Used in computer science and information theory
Antilog is useful whenever you need to convert from a logarithmic scale back to a linear scale. This comes up constantly in science and engineering, from measuring sound intensity to calculating compound interest.
General Formula
antilogb(x) = bx
Common Antilog (Base 10)
antilog10(x) = 10x
Example: antilog10(3) = 103 = 1000
Natural Antilog (Base e)
antiloge(x) = ex
Example: antiloge(2) = e2 ≈ 7.389
Binary Antilog (Base 2)
antilog2(x) = 2x
Example: antilog2(4) = 24 = 16
| Logarithm | Result | Antilog | Returns |
|---|---|---|---|
| log10(100) | = 2 | antilog10(2) | = 100 |
| log10(1000) | = 3 | antilog10(3) | = 1000 |
| log10(0.1) | = -1 | antilog10(-1) | = 0.1 |
| log10(1) | = 0 | antilog10(0) | = 1 |
| ln(e) | = 1 | antiloge(1) | = e ≈ 2.718 |
Converting Logarithmic Scales Back to Linear
Many scientific measurements use logarithmic scales to handle huge ranges of values. Antilog converts these back to meaningful linear values you can actually use in calculations.
pH Calculations
pH is defined as -log10[H+]. To find the hydrogen ion concentration from pH, you calculate [H+] = 10-pH. A pH of 3 means [H+] = 10-3 = 0.001 mol/L.
Decibel Calculations
Sound intensity in decibels uses the formula dB = 10 log10(P/P0). To find the actual power ratio from decibels, use P/P0 = 10dB/10. A 20 dB increase means 102 = 100 times more power.
Earthquake Magnitude (Richter Scale)
The Richter scale is logarithmic. Each whole number increase represents 10 times greater amplitude. The energy release follows E = 101.5M + 4.8 joules, where M is magnitude. A magnitude 6 quake releases about 1013.8 joules.
Financial Calculations
Compound interest calculations often use natural logarithms to solve for time or rate. When you need to convert back, antilog (specifically ex) gives you the actual growth factor. For continuous compounding: A = Pert.
What is antilog?
Antilog is the inverse operation of a logarithm. If you take the logarithm of a number, taking the antilog of that result gives you back the original number. Mathematically, antilogb(x) = bx.
How do you calculate antilog?
To calculate antilog, raise the base to the power of the given value. For common antilog (base 10), calculate 10x. For natural antilog, calculate ex. Most calculators have dedicated buttons: 10x for common antilog and ex for natural antilog.
What is the difference between log and antilog?
Log and antilog are inverse operations. Logarithm finds the exponent: logb(x) asks "what power do I raise b to get x?" Antilog finds the result: antilogb(y) asks "what do I get when I raise b to the power y?" They undo each other.
Can antilog be negative?
The result of an antilog calculation is always positive when using a positive base. This is because any positive number raised to any real power always produces a positive result. However, the input value (the exponent) can be negative, which gives a fractional result between 0 and 1.
What is the antilog of 0?
The antilog of 0 is always 1, regardless of the base (as long as the base is positive and not 1). This is because any number raised to the power of 0 equals 1. So antilog10(0) = 100 = 1, and antiloge(0) = e0 = 1.
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