Exponent Calculator. Step-by-step solution

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Last update: 2024-06-18

5/1

Base

Exponent

Result:

2.2133638394007

Solution steps

Initial approximation:

Result: 1
Term: 1

Calculating the logarithm

log (base)

log(24)

= 3.178053830348

Multiply the exponent by the logarithm

0.25 × 3.178053830348

= 0.79451345758701

Use Taylor series:

f (x) = \sum_{n = 0}^{\infty} (\frac{f^{(n)} (a)}{n!} ​) {(x - a)}^{n}

Term = 0.79451345758701^(0 × 2 - 1) ÷ (0 × 2 - 1) = 0.79451345758701
Result = 1 + 0.79451345758701 = 1.794513457587

= 1.794513457587

Term = 0.79451345758701^(1 × 2 - 1) ÷ (1 × 2 - 1) = 0.31562581714343
Result = 1 + 0.31562581714343 = 2.1101392747304

= 2.1101392747304

Term = 0.79451345758701^(2 × 2 - 1) ÷ (2 × 2 - 1) = 0.083589653094117
Result = 1 + 0.083589653094117 = 2.1937289278246

= 2.1937289278246

...

Term = 0.79451345758701^(16 × 2 - 1) ÷ (16 × 2 - 1) = 5.6318731788114E-17
Result = 1 + 5.6318731788114E-17 = 2.2133638394007

= 2.2133638394007

Iterations: 17

= 2.2133638394007

Rating: 5

Votes: 1

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