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Cogito

Integrated Math 3 · Chapter 4 · Lesson 3

Practice Worksheet

Solving Exponential and Logarithmic Equations

Getting the unknown out of the exponent.

12 problems · about 22 minutes · F-LE.A.4, A-REI.D.11

NameDate

Figure — use these to answer the problems

Solving an exponential equation asks where this curve reaches a given height.
-8-8-6-6-4-4-2-222446688
y = 1 · 2^x + 0
  • Point(2, 4)
a1
b2
Point on the curve2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. 4ˣ = 64. What is x?

    Answer

  2. Why must log equation solutions be checked?

    • Combining logs can widen the domain, admitting invalid values.
    • Because of rounding errors.

  3. 2ˣ = 64. What is x?

    Answer

  4. 3ˣ = 81. What is x?

    Answer

  5. log base 3 of x = 2. What is x?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. log base 5 of x = 3. What is x?

    Answer

  2. 5ˣ = 1. What is x?

    Answer

  3. A candidate makes a log argument negative. Is it valid? 1 yes, 0 no.

    Answer

Stretch Yourself

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

4 problems

  1. Put the solving process for a log equation in order.

    Write 1 to 4 in the boxes to put these in order.

    • Use the laws to combine into a single logarithm.
    • Rewrite in exponential form.
    • Solve the resulting equation.
    • Reject any candidate that makes an argument non-positive.

  2. 10ˣ = 1000. What is x?

    Answer

  3. The Same Base

    2ˣ = 32. What is x?

    Answer

  4. The Log Equation

    log base 2 of x = 4. What is x?

    Answer