Musings on the HP-70

[Thomas Klemm]

Natural Logarithm

Example

\(
\log(1.2) = \log(1 + 0.2) \approx 0.182321557
\)

Initialisation

DSP 9
-1
STO K
0.2
ENTER
ENTER
ENTER
11
STO M
÷

Loop

1
K
M+
÷
x<>y
-
×


Result

0.018181818
0.016363636
0.018949495
0.021210101
0.024329408
0.028467452
0.034306510
0.043138698
0.058038927
0.088392215
0.182321557


Explanation

\(
\begin{aligned}
\log(1+x)
&= x-{\frac {x^{2}}{2}}+{\frac {x^{3}}{3}} - \cdots \\
&= x \cdot \left(\frac{1}{1} - x \cdot \left(\frac{1}{2} - x \cdot \left(\frac{1}{3} - \cdots \right) \right) \right)
\end{aligned}
\)

Python Program

Code:

x = 0.2
s = 0
for k in range(11, 0, -1):
    s = x * (1 / k - s)
    print(f"{s:>.9f}")

References

• Taylor series