Three Real Properties, and the Fakes That Cost Points

You'll learnto use the three real logarithm properties and refuse the fake ones.

Logs have exactly three algebraic moves — products add, quotients subtract, powers lift out front — and each one is an exponent rule wearing a disguise. Everything else students “remember” is a fake. Watch the real properties assemble from stacked exponent blocks, then watch log(8+8) detonate the most expensive fake in the unit. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · PRODUCTS ADD · POWERS LIFT · SUMS STAY · v4

products add · powers lift · sums do nothing

Before you start

What you're looking at

Towers of blocks on a baseline: each tower is as tall as the exponent it stands for.

The question

What does a log do to a product, a quotient, and a power inside it?

Step 1 / 12