Exponential and Logarithmic Functions
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Tap a term to see what it means, or .
Calculate
Example: a population doubles each generation, so after x generations it is 2ˣ times the original. How much is it after 3 generations — and how many generations make it 8 times? Change the values to work out your own case; a base between 0 and 1 gives decay.
Step by step
What each term means
- Exponential (y = bˣ)
- The base multiplied by itself x times — and, for fractional or negative x, the continuous extension of that. Each step of 1 in x multiplies y by b.
- Logarithmic (x = log_b y)
- The reverse question: to what power must b be raised to reach y? The two functions undo each other, and their graphs mirror each other in the line y = x.