Cogito
Integrated Math 3 · Chapter 4 · Lesson 2
Logarithms and Their Laws
The inverse of an exponential.
12 problems · about 21 minutes · F-BF.B.4, F-LE.A.4
What this lesson teaches
The student defines logarithms and applies the logarithm laws.
- A logarithm answers what exponent produces a value.
- It is the inverse of an exponential, so the domain is positive numbers only.
- The laws are the exponent rules read backwards.
Warm Up
Straightforward practice. Get the method working first.
5 problemsWhat is log base 4 of 16?
Answer 2
Why 2.
Is the log of a sum the sum of the logs?
Answer No. Only products and quotients split.
Why Logs do not distribute over addition.
log base 3 of 9?
Answer 2
Why 3² = 9.
log base 5 of 125?
Answer 3
Why 5³ = 125.
log base 10 of 1?
Answer 0
Why Anything to the zero.
Build It Up
The same ideas with more to keep track of.
3 problemslog 12 − log 3 equals log of what number?
Answer 4
Why 12 ÷ 3.
log(x⁵) equals k times log x. What is k?
Answer 5
Why The power law.
Can a logarithm take a negative input? 1 yes, 0 no.
Answer 0
Why An exponential is never negative.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMatch each log law with the exponent rule behind it.
Answer Log of a product is a sum → Multiplying powers adds exponents; Log of a quotient is a difference → Dividing powers subtracts exponents; Log of a power brings the exponent out → A power of a power multiplies exponents
Why Each law mirrors one exponent rule.
log base 2 of 64?
Answer 6
Why 2⁶ = 64.
The Definition: What is log base 2 of 8?
Answer 3
Why 3.
The Product: log 4 + log 25 equals log of what number?
Answer 100
Why 100.