Calculator for Power and Root

Perform exponentiation using power calculations, square roots, and logarithms. Exponentiation or power is repeated multiplication in succession. For example, 2³ = 2*2*2 = 8. 2³ is pronounced "two to the power of three". Root is an inverse operation of power. The above calculation, reversed, is ³√8 = 2. ³√8 is pronounced "the third root of eight".
The logarithm is another inverse operation of exponentiation, which returns the exponent rather than the base. Applied to the above example, the calculation is log₂8 = 3. The expression log₂8 is pronounced "logarithm to the base two of eight".

Precision: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 decimal places.

Power, calculations in the form a^b

  a:

  b:

a^b:



   

The power of 2 is also called a square, and the power of 3 is called a cube. These very common values ​​are entered using the corresponding buttons.

Roots, calculations in the form ^b√a

   a:

   b:

^b√a:



   

The second root is often simply called a root, but the more specific term is square root. The third root is called the cube root.

Logarithm, calculations in the form log_b(a)

          a:

          b:

log_b(a):



   

The logarithm to base 2 is the dual logarithm ld. The logarithm to base e is the natural logarithm ln. The logarithm to base 10 is the decimal logarithm lg.

Of course, numbers can be entered in every field, with a comma or point as the decimal separator. Also allowed is e for Euler's number, approximately 2.718281828459045. The arithmetic operations +, - *, and / or :, as well as parentheses ( ) are also allowed, for mathematical formulas.

Euler's number e is a special value in many ways. For example, the exponential function e^x is the only function that is equal to its derivative. Euler's number can be defined, among other things, as e = (1+1/n)n for lim n → ∞, or as the infinite sum of the reciprocals of the factorials of the natural numbers, e = Σ 1/k!

Last updated on 07/01/2025. Author: Jürgen Kummer

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