Logarithm Calculator

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Last update: 2024-06-18
0/0
Result:
3.178053830348
Solution steps
1.
Calculate the logarithm of the base. Variable logBase
1.
x = base - 1 base + 1
x = (2.718281828459 - 1) ÷ (2.718281828459 + 1)
1.
(2.718281828459 - 1) ÷ (2.718281828459 + 1)
2.718281828459 - 1
= 1.718281828459
2.
1.718281828459 ÷ (2.718281828459 + 1)
2.718281828459 + 1
= 3.718281828459
3.
1.718281828459 ÷ 3.718281828459
1.718281828459 ÷ 3.718281828459
= 0.46211715726
= 0.46211715726
2.
Use Taylor series: f ( x ) = n = 0 ( f ( n ) ( a ) n! ) ( x - a ) n
Where:
Function: f ( x , i ) = x i × 2 - 1 i × 2 - 1
x: 0.46211715726
i: Iteration number 1, 2, 3, ..., n
Initial result: 0
Initial term: 0
1.
Term = 0.46211715726^(1 × 2 - 1) ÷ (1 × 2 - 1) = 0.46211715726
Result = 0 + 0.46211715726 = 0.46211715726
= 0.46211715726
2.
Term = 0.46211715726^(2 × 2 - 1) ÷ (2 × 2 - 1) = 0.03289538885607
Result = 0.46211715726 + 0.03289538885607 = 0.49501254611607
= 0.49501254611607
3.
Term = 0.46211715726^(3 × 2 - 1) ÷ (3 × 2 - 1) = 0.0042149309191085
Result = 0.49501254611607 + 0.0042149309191085 = 0.49922747703518
= 0.49922747703518
4.
...
5.
Relative change: 8.8817841970015E-16 < Dynamic Epsilon: 1.0E-15 = Stopping calculations
= 0.49999999999999
6.
Iterations: 21
= 0.49999999999999
2.
Calculate the logarithm of the x. Variable logX
1.
x = x - 1 x + 1
x = (24 - 1) ÷ (24 + 1)
1.
(24 - 1) ÷ (24 + 1)
24 - 1
= 23
2.
23 ÷ (24 + 1)
24 + 1
= 25
3.
23 ÷ 25
23 ÷ 25
= 0.92
= 0.92
2.
Use Taylor series: f ( x ) = n = 0 ( f ( n ) ( a ) n! ) ( x - a ) n
Where:
Function: f ( x , i ) = x i × 2 - 1 i × 2 - 1
x: 0.92
i: Iteration number 1, 2, 3, ..., n
Initial result: 0
Initial term: 0
1.
Term = 0.92^(1 × 2 - 1) ÷ (1 × 2 - 1) = 0.92
Result = 0 + 0.92 = 0.92
= 0.92
2.
Term = 0.92^(2 × 2 - 1) ÷ (2 × 2 - 1) = 0.25956266666667
Result = 0.92 + 0.25956266666667 = 1.1795626666667
= 1.1795626666667
3.
Term = 0.92^(3 × 2 - 1) ÷ (3 × 2 - 1) = 0.13181630464
Result = 1.1795626666667 + 0.13181630464 = 1.3113789713067
= 1.3113789713067
4.
...
5.
Relative change: 0 < Dynamic Epsilon: 1.0E-16 = Stopping calculations
= 1.589026915174
6.
Iterations: 186+
= 1.589026915174
3.
log e ( 3 ) = logX logBase
1.589026915174 ÷ 0.49999999999999
= 3.178053830348
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