Algebra
Doublings to reach a target
The base-2 logarithm of the growth ratio. It counts how many times the starting value must double to reach the target.
The Formula
n = ln(target / start) / ln(2)
The base-2 logarithm of the growth ratio. It counts how many times the starting value must double to reach the target.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| S | Starting value | dimensionless | Where the growth begins. |
| T | Target value | dimensionless | Where it ends. |
| n | Doublings | doublings | Number of doublings needed, not necessarily a whole number. |
What Each Symbol Means
Sdimensionless
Starting value
Where the growth begins.
Tdimensionless
Target value
Where it ends.
ndoublings
Doublings
Number of doublings needed, not necessarily a whole number.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a logarithm page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Logarithm, filed under Math. Every number the guide produces comes from substituting into this one line.