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Cogito

AP Precalculus · Chapter 5 · Lesson 2

Practice Worksheet

Logarithms as Inverses

The question an exponential cannot answer.

12 problems · about 22 minutes · AP Precalculus 2.7, 2.8, 2.10

NameDate

Figure — use these to answer the problems

The curve rises fast then flattens, and never reaches the vertical axis. That edge is the domain restriction.
-8-8-6-6-4-4-2-222446688
y = 1 ln x + 0
  • Point(2, 0.69)
a, coefficient1
Point on the curve2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. What is log base 4 of 64?

    Answer

  2. Why can a logarithm not take a negative input?

    • An exponential output is always positive, so nothing maps back from a negative.
    • It is an arbitrary convention.

  3. log base 3 of 9?

    Answer

  4. log base 5 of 125?

    Answer

  5. log base 10 of 1?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. log 8 minus log 2 equals log of what number?

    Answer

  2. log(x³) equals k times log x. What is k?

    Answer

  3. Can a logarithm take a negative input? 1 yes, 0 no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Match each log law with the exponent rule behind it.

    Draw a line from each item on the left to its match on the right.

    • Log of a product is a sum
    • Log of a quotient is a difference
    • Log of a power brings the exponent out
    • Multiplying powers adds exponents
    • Dividing powers subtracts exponents
    • A power of a power multiplies exponents

  2. log base 2 of 32?

    Answer

  3. The Definition

    What is log base 2 of 8?

    Answer

  4. The Product Law

    log 4 + log 25 equals log of what number?

    Answer