Exponent Calculator. Step-by-step solution

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Last update: 2024-06-18

5/1

Base

Exponent

Result:

1.4028505520067

Solution steps

Initial approximation:

Result: 1
Term: 1

Calculating the logarithm

log (base)

log(15)

= 2.7080502011023

Multiply the exponent by the logarithm

0.125 × 2.7080502011023

= 0.33850627513778

Use Taylor series:

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

Term = 0.33850627513778^(0 × 2 - 1) ÷ (0 × 2 - 1) = 0.33850627513778
Result = 1 + 0.33850627513778 = 1.3385062751378

= 1.3385062751378

Term = 0.33850627513778^(1 × 2 - 1) ÷ (1 × 2 - 1) = 0.057293249153829
Result = 1 + 0.057293249153829 = 1.3957995242916

= 1.3957995242916

Term = 0.33850627513778^(2 × 2 - 1) ÷ (2 × 2 - 1) = 0.0064647081205345
Result = 1 + 0.0064647081205345 = 1.4022642324121

= 1.4022642324121

...

Term = 0.33850627513778^(12 × 2 - 1) ÷ (12 × 2 - 1) = 1.2305155172725E-16
Result = 1 + 1.2305155172725E-16 = 1.4028505520067

= 1.4028505520067

Iterations: 13

= 1.4028505520067

Rating: 5

Votes: 1

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