ransform a formula for doubling time I have a problem with transforming a formula for doubling time

Boilanubjaini8f

Boilanubjaini8f

Answered question

2022-06-07

ransform a formula for doubling time
I have a problem with transforming a formula for doubling time. It has two variables: increase (i) and number of periods (p).
The original formula: p = log ( 2 ) log ( 1 + i )
When I enter i = 0.05 it correctly calculates p = 14.207
Now I'm trying to make a formula for "increase". I transformed it to: i = 10 log ( 2 ) p 1.. When I enter 14.207 periods, it gives me a increase = 0.1189 (and not 0.05). Where's my mistake?
The transformations I did:
p = log ( 2 ) log ( 1 + i )
log ( 1 + i ) = log ( 2 ) p
1 + i = 10 log ( 2 ) p
i = 10 log ( 2 ) p 1
It gives a wrong answer... Do you see where I made a mistake?

Answer & Explanation

Odin Jacobson

Odin Jacobson

Beginner2022-06-08Added 17 answers

It is using logarithm base e. That didn't matter in the first formula, because the difference was cancelled by the two logarithms.
Two solutions: 1) there might be a logarithm spelt 'log10' instead of 'log'
Or, 2) you could use exp ( log ( 2 ) / p ) 1

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