Understanding Logarithms
Logarithms tend to show up maybe once per test, if that. They're reverse exponents. If you're comfortable with exponents, learning logarithms won't be a big leap.
Keep in mind this sort of question tends to show up once per test, if that. Use your best discretion to decide how much time, if any, you should spend on this page.
Consider this Example
Question:
Is the same as asking: 2 to what power is 8?
Which can be expressed as:
Just for clarity's sake, the answer is 3. because (2 * 2 * 2) = 8.
The point is, this is the logic ACT® will use to ask about logarithms.
Now, what if instead of , you saw on the test? If we didn't have the context above, then that question might seem a little hard to conceptualize. We could rewrite it as . Then the problem is just a simple exponent question.
Question:
- A) 2
- B) 3
- C) 4
- D) 5
- E) 6
Click for the Answer
Correct Answer: B. 3
Explanation:
- A) 2: This answer implies that 3^2 = 27, which is incorrect because 3^2 = 9.
- B) 3: This is correct because 3^3 = 27.
- C) 4: This answer implies that 3^4 = 27, which is incorrect because 3^4 = 81.
- D) 5: This answer implies that 3^5 = 27, which is incorrect because 3^5 = 243.
- E) 6: This answer implies that 3^6 = 27, which is incorrect because 3^6 = 729.
Question:
- A) 8
- B) 12
- C) 16
- D) 20
- E) 24
Click for the Answer
Correct Answer: C. 16
Explanation:
- A) 8: This answer implies that 4^2 = 8, which is incorrect because 4^2 = 16.
- B) 12: This answer implies that 4^2 = 12, which is incorrect because 4^2 = 16.
- C) 16: This is correct because 4^2 = 16.
- D) 20: This answer implies that 4^2 = 20, which is incorrect because 4^2 = 16.
- E) 24: This answer implies that 4^2 = 24, which is incorrect because 4^2 = 16.
How will this show up on the ACT® Math Test?
You'll typically see logarithm questions on the ACT® Math section in formats similar to the examples. They're seldom more complicated than the given examples. If you understand the rules behind logarithms, you can use them to solve questions for a missing part.