e Calculator - eˣ, Euler's Number Raised to Power x

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Forward mode computes e raised to the power x. Inverse mode finds the natural log of y, which is the x such that eˣ = y.
The exponent x in eˣ. Accepts any real number: positive, negative, zero, or fractional.
Number of terms to include in the Taylor series approximation shown in the steps panel. More terms give a closer approximation.
terms
Left boundary of x for the exponential curve chart.
Right boundary of x for the exponential curve chart.
eˣ
7.3890561

Euler's number e raised to the power x

Taylor approximation7.38095238
Taylor error0.008103718
e^(-x) = 1/eˣ0.13533528
sqrt(eˣ) = e^(x/2)2.71828183
7.3890561>99.9% below · x

e^2 = 7.389056

  • e^2 = 7.389056: the exponential function grows rapidly for positive x.
  • The reciprocal is e^(-2) = 0.13533528, because e^x * e^(-x) = e^0 = 1.
  • The square root of e^x is e^(2/2) = e^(1.0000) = 2.71828183.
  • The 8-term Taylor series approximates e^x as 7.380952, with an error of 8.104e-3.

Next stepTo reverse this: ln(7.3891) = 2. Switch to ln(y) mode and enter the result to verify.

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