Factors In, Amounts Out

You'll learnto recognize a logarithmic model from equal input factors giving equal output steps.

Multiply the input by ten and the output climbs by the same three units — every single time. That is the logarithmic signature, the exponential story run backward, and it is how pH, decibels and earthquake magnitudes compress universes of scale into small friendly numbers. The trap: reading a and b in a + b·log(x) with their jobs swapped. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · f(x) = a + b·log(x) · v3

multiply the input · step the output

Before you start

What you're looking at

A table drawn as a chart, where the inputs multiply by ten while the outputs add three.

The question

The inputs multiply and the outputs add — which family is that?

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