Formula and example
How it is calculated
b^(ax+c)=d: x=[ln(d)/ln(b)−c]/a. log_b(ax+c)=d: x=(b^d−c)/a.
Worked example
2^x=8 gives x=3. For log₂(2x+1)=3, we obtain 2x+1=8 and therefore x=3.5.
Things to check
- The base must be positive and different from 1. For the exponential equation, d must be positive.
- This calculator handles the two stated basic forms, rather than arbitrary mixed equations.
Frequently asked questions
Are bases between 0 and 1 allowed?
Yes. The logarithm is then decreasing, but the transformations remain valid as long as all domain conditions are met.