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 multiply 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 exponents, then watch log(8+8) detonate the most expensive fake in the unit.

8 STEPS · 6 QUICK CHECKS · products add · powers lift · sums stay · DOMAIN CONDITIONS · v3

log properties

Before you start

What you're looking at

A three-rule card — product adds, quotient subtracts, power comes out front — with a red 'no sum rule' warning.

The question

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

Watch for

The three legal moves in a single base, and log(8+8) detonating the most expensive fake in the unit.

Step 1 / 8