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Cogito

Algebra 2 · Chapter 6 · Lesson 2

Practice Worksheet

The Laws of Logarithms

Turning products into sums.

11 problems · about 23 minutes · F-LE.A.4, A-SSE.B.3

NameDate

Figure — use these to answer the problems

A logarithm grows without limit, but ever more slowly.

y = 1 ln x + 0

a1

Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

log base 3 of 81. What is it?
Answer
log base 3 of 9. What is it?
Answer
log base 5 of 125. What is it?
Answer
log base 10 of 1. What is it?
Answer

Build It Up

The same ideas with more to keep track of.

3 problems

log(x⁷) equals what multiple of log x?
Answer
log base 2 of 32. What is it?
Answer
7
Match each expression to its expanded form.
Draw a line from each item on the left to its match on the right.
- log(xy)
- log(x / y)
- log(xⁿ)
- log x + log y
- log x − log y
- n log x

Stretch Yourself

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

4 problems

Is log(x + y) the same as log x + log y? 1 for yes, 0 for no.
Answer
log base 4 of 16. What is it?
Answer
The Power
log(x⁵) equals what multiple of log x?
Answer
A Value
log base 2 of 8. What is it?
Answer