RPN: HP 11C: Transferring Between Bases (Common/Natural)
All algorithms were tested with the HP 11C.
Between the Exponential Function and Common-Antilog
e^α = 10^ß
Given α, what is ß?
ß = log(e^α)
RPN:
<input α>
e^x
LOG
Examples (Fix 6):
e^1.05 = 10^ß
ß ≈ 0.456009
e^(-2.2) = 10^ß
ß ≈ -0.955448
Given ß, what is α?
α = ln(10^ß)
RPN:
<input ß>
10^x
LN
Examples (Fix 6):
e^α = 10^5.4
α ≈ 12.433960
e^α = 10^0.366
α ≈ 0.842746
Between the Natural Logarithm and Common Logarithm
log α = ln ß
Given α, what is ß?
ẞ = exp(log α)
RPN:
<input α>
LOG
e^x
Examples (Fix 6):
log 17 = ln ß
ß ≈ 3.422766
log 317 = ln ß
ß ≈ 12.195405
Given ß, what is α?
α = 10^(ln ß)
RPN:
<input ß>
LN
10^x
Examples (Fix 6):
log α = ln 425
α ≈ 1,127,428.915
log α = ln 9.81
α ≈ 192.044677
Eddie
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