What you'll practice

A logarithm asks for an exponent: $\log_b x$ means "$b$ to what power gives $x$?". These questions cover whole-number powers ($\log_3 81$), fractional results ($\log_5 \frac{1}{25}$), common logs (base 10), and the special values $\log_b 1 = 0$ and $\log_b b = 1$.

Worked example

Common mistakes

• Dividing instead of taking a power: $\log_2 32 \neq 16$. The log is the EXPONENT, not the quotient.
• Fractions mean negative exponents: $\log_5 \frac{1}{25} = -2$ because $5^{-2} = \frac{1}{25}$ — not $\frac{1}{2}$.
• Forgetting the plain log is base 10: $\log 1000 = 3$ because $10^3 = 1000$.

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FAQ

How do you evaluate a logarithm?

Rewrite it in exponent form and answer that question instead: log₂ 32 asks 2 to what power gives 32 — count powers of 2 up to 32 and you get 5. For fractions, expect a negative exponent; a plain log means base 10.

What does a logarithm actually mean?

It's an exponent. log base b of x asks: b raised to what power equals x? Rewriting every log question in exponent form makes it concrete.

Why is the log of 1 always 0?

Because any base raised to the 0 power is 1. Similarly the log base b of b is always 1, since b to the first power is b.

Is Cramzoo free?

Cramzoo is free to start — every unit opens with free skills and no account is needed. This particular skill is part of Premium ($6/month or $30/year), which unlocks every skill plus the parent progress dashboard.

How is this different from IXL?

No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is double-checked for accuracy before it reaches you.

Related Algebra 2 skills

• Solve exponential equations