What you'll practice

When both sides of an equation can be written with the same base, the exponents must be equal: $2^{x+1} = 16$ becomes $2^{x+1} = 2^4$, so $x + 1 = 4$. These questions cover recognizing powers, rewriting fractions as negative exponents, and mismatched bases that share a common base (like $4$ and $8$ as powers of $2$).

Worked example

Common mistakes

• Dividing by the base: $2^x = 16$ is not solved by $x = 8$. Match bases and compare exponents instead.
• Fraction panic: $2^x = \frac{1}{8}$ has the clean answer $x = -3$, because $\frac{1}{8} = 2^{-3}$.
• Missing a shared base: $4^x = 8$ looks stuck until both become powers of 2: $2^{2x} = 2^3$, so $x = \frac{3}{2}$.

Try a few

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FAQ

How do you solve an exponential equation without logarithms?

Write both sides as powers of the same base; then the exponents must be equal, and you solve that simpler equation. This works whenever both sides are exact powers of a common base.

What if the bases can't be matched?

Then logarithms take over — take the log of both sides. Base-matching is the fast path; logs are the general one.

Is Cramzoo free?

Yes — this skill is one of the free ones. Every unit opens with free skills, no account needed. Premium ($6/month or $30/year) 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 reviewed by a human before you see it.

Related Algebra 2 skills

• Evaluate logarithms