Cogito
Algebra 2 · Chapter 6 · Lesson 2
The Laws of Logarithms
Turning products into sums.
11 problems · about 23 minutes · F-LE.A.4, A-SSE.B.3
What this lesson teaches
The student applies the product, quotient, and power laws of logarithms.
- A product inside a logarithm becomes a sum outside it.
- A quotient becomes a difference, and a power becomes a multiplier.
- The laws mirror the exponent laws because a logarithm is an exponent.
Warm Up
Straightforward practice. Get the method working first.
4 problemslog base 3 of 81. What is it?
Answer 4
Why 4.
log base 3 of 9. What is it?
Answer 2
Why 3² = 9.
log base 5 of 125. What is it?
Answer 3
Why 5³.
log base 10 of 1. What is it?
Answer 0
Why Anything to the power nought.
Build It Up
The same ideas with more to keep track of.
3 problemslog(x⁷) equals what multiple of log x?
Answer 7
Why Bring it down.
log base 2 of 32. What is it?
Answer 5
Why 2⁵.
Match each expression to its expanded form.
Answer log(xy) → log x + log y; log(x / y) → log x − log y; log(xⁿ) → n log x
Why They mirror the exponent laws exactly.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsIs log(x + y) the same as log x + log y? 1 for yes, 0 for no.
Answer 0
Why The law is about products.
log base 4 of 16. What is it?
Answer 2
Why 4².
The Power: log(x⁵) equals what multiple of log x?
Answer 5
Why 5.
A Value: log base 2 of 8. What is it?
Answer 3
Why 3.