Every Root Walks Back Through the Gate

You'll learnto free an unknown from an exponent or a logarithm, and to send every candidate root back through the domain gate.

Two locks and two keys: taking a logarithm frees an unknown stuck in an exponent, and raising the base frees one stuck inside a logarithm. The algebra is four lines, and it is not where the points go. They go on the move that condenses two logs with a property that does not exist, and on trusting a root the original equation refuses to accept. Watch a root get turned away at the door. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · log₂(x) + log₂(x−6) = 4 · v4

two keys · and one door every answer has to walk back through

Before you start

What you're looking at

Equations rewritten one line at a time, then a number line where candidate roots walk toward the point past which the logarithms exist.

The question

Is the unknown stuck in an exponent or inside a logarithm, and does the answer survive the original equation?

Step 1 / 12