\[x=\frac{\ln(y/a)}{\ln(b)}\]
Variables
xsolution variable
yresult value
ainitial coefficient
bexponential base
Description
What is this formula?
This formula explicitly solves an exponential equation of the form:
y=ab^x
It calculates the exponent x using logarithms.
When to use it
Use this formula when the unknown variable appears as an exponent.
Example
For:
32=2*2^x
The solution is:
x=4
Applications
- Exponential growth analysis
- Population models
- Radioactive decay
- Financial compound growth
- Engineering calculations