Exponents, Exponentials and Logarithms · Overview

Exponents, Exponentials and Logarithms

Exponent questions ask you to simplify products, quotients and powers with negative and fractional exponents, and to evaluate numbers such as 27−2/327^{-2/3} by hand. Exponential questions ask you to build or read a model such as a(1+r)ta(1 + r)^t, including doubling and half-life models.

Logarithm questions ask what a log means (log⁡bx=y\log_b x = y means by=xb^y = x), use the product, quotient and power rules, and solve equations where the unknown is an exponent or sits inside a log. The last step is often a domain check that throws out an extraneous root.

How often it appears

The Math section has 45 questions in 50 minutes, about 67 seconds each, with four answer choices. Exponent rules count toward Number and Quantity (10–12% of the section), exponential models and logs toward Functions (17–20%), and exponential equations toward Algebra (17–20%).

Expect these ideas in a few questions per test, and as single steps inside longer modeling and function questions, so the skills here pay off across several categories.

The question you’ll see

If log⁡2(x+1)=4\log_2(x + 1) = 4, what is the value of xx?

In this module

  1. Overview Paid
  2. Exponent rules Paid
  3. Exponential growth and decay Paid
  4. What a logarithm means Paid
  5. Log properties Paid
  6. Solving exponential and log equations Paid
  7. Strategy summary Paid
  8. Mastery quiz Paid
  9. Pace check Paid