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.

8 STEPS · 6 QUICK CHECKS · f(x) = a + b·log(x) · v2

×10 in → +b out

Before you start

What you're looking at

A table where the inputs multiply by ten while the outputs add three, with arrows drawn on both columns.

The question

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

Watch for

The three family signatures side by side, and the a-versus-b swap in a + b·log(x).

Step 1 / 8