Exponential function calculator
Calculator for common operations related to exponential function.

Beta version#

BETA TEST VERSION OF THIS ITEM
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Symbolic algebra

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

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Calculations data - enter values, that you know here#

Function value (yy)
(the function value at single point x, often marked as f(x))
=>
Value of exponent function (exp(x)exp(x))
=>
Function argument (xx)
<=
Base of the exponential function (aa)
<=

Result: function value (yy)#

Summary
Used formulaShow sourcey=ax y={ a}^{ x}
ResultShow source11
Numerical resultShow source11
Result step by step
1Show source11{1}^{1}Removed exponent by one
2Show source11Result
Numerical result step by step
1Show source11Result

Some facts#

  • Exponential function is a function that can be presented in the form:
    y=ax y={ a}^{ x}
    where:
    • yy - function value (the function value at single point x, often marked as f(x)),
    • xx - function argument (called also independent value),
    • aa - base of the exponential function.
  • A special case is the exponential function of the base e (→ see the number e):
    exp(x)=ex exp(x)={ e}^{ x}
  • The exponential function with the base e is often denoted as exp (x), which we read as exponent of x.
  • The inverse function for the exponential one is logarithmic function. In particular for the function exp(x) (the base is number e) the inverse function is natural logarithm.
  • The exponential function has no zero poins. Its all values ​​are located above the OX axis (all function values are positive).
  • Depending on the base a, we can distinguish three scenarios:
    • base is less than one (a <1) - function is decreasing,
    • base is greater than one (a > 1) - the function is inreasing,
    • base is equal to zero (a = 0) - the function is reduced to constant function.

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