Every Root Walks Back Through the Gate

You'll learnto solve the two kinds of exp/log equation and check every root at the domain gate.

Two locks, two keys: a logarithm frees a trapped exponent, and exponentiating frees a trapped log argument. The algebra is four lines. The points die elsewhere — condensing with a fake property, and trusting a candidate root the original equation refuses to accept. Watch a root get executed at the domain gate.

8 STEPS · 6 QUICK CHECKS · log₂(x) + log₂(x−6) = 4 · v3

condense · convert · check

Before you start

What you're looking at

Two separate short stories: an unknown trapped in an exponent, and an unknown trapped inside a logarithm.

The question

Is the unknown stuck in an exponent, or inside a logarithm?

Watch for

Each type's one-line key, the domain gate set before solving, and a candidate root getting rejected there.

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