Free · Exponents and logarithms
Powers of 2 & Reverse Logarithms
Find 2 raised to a real exponent, or recover the exponent from a positive result using a base-2 logarithm.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
2 raised to 3 is 8. The reverse calculation asks which exponent produces a positive number: log base 2 of 8 is 3.
y = 2^x; x = ln(y) / ln(2)
Worked example
Enter these known values and leave the other values blank.
- Exponent x
- 3
- Result 2^x
- 8
Assumptions and limitations
- The base stays fixed at 2. Enter either the exponent or the positive result; the other field is calculated.
- Zero and negative exponents are valid. An exponent of zero produces 1, and a negative exponent produces a reciprocal.
- A finite real exponent produces a strictly positive result. Zero and negative results have no real logarithm.
- The supported exponent interval is −1000 through 1000, including reverse results.
- Values use finite numerical precision. Display rounding does not turn a very small positive result into mathematical zero.
Common questions
Can the exponent be a decimal?
Yes. For example, 2^0.5 is the positive square root of 2.
Why is a zero result invalid?
No finite real exponent makes 2^x equal zero. The values approach zero as x decreases, but never reach it.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.
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