ACT exponents and logarithms strategies
Exponents and logarithms test your ability to manipulate expressions with powers and logarithmic relationships. These strategies cover the exponent rules, logarithm properties, and a step-by-step approach to solving exponential and logarithmic equations.
The core principle
Exponents are repeated multiplication. When you multiply two powers with the same base, you add the exponents. When you divide, you subtract. When you raise a power to a power, you multiply. Logarithms are the inverse of exponentiation: they ask what exponent produces a given result.
The most common trap
Multiplying exponents when you should add them
When multiplying powers with the same base, add the exponents. When raising a power to a power, multiply the exponents. The answer choices include the wrong operation because the test writers know this mistake.
Step-by-step strategy
When to use: any question involving exponents or logarithms.
- 1Identify the base. If bases match, apply the exponent rules directly.
- 2If bases do not match, try to rewrite them so they do (e.g., 4 = 2 squared).
- 3For logarithms, convert between exponential and logarithmic form using the definition.
- 4Check the answer choices for the result of the wrong operation.
Related pages
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