The Exponent Question

You'll learnto read a logarithm as the question 'what exponent turns the base into the argument?'

Every logarithm asks one question: what exponent turns the base into the argument? Hold that sentence and log expressions stop being a symbol game. Watch the three roles trade costumes between exponential and log form, climb the doubling ladder above and below zero, and catch the “rule” for log of a sum that has never existed.

8 STEPS · 6 QUICK CHECKS · log_b(c) = a ⇔ bᴸ = c · v2

log₂

Before you start

What you're looking at

A logarithm with its base, exponent, and result color-coded into three roles.

The question

What power of the base produces the argument?

Watch for

The three roles swapping places between exponential and log form, and the doubling ladder dropping below zero.

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