6.5: Properties of Logarithms
Properties of logarithms you should care about:
1. Use properties of logarithms to expand each expression
completely:
a. log 4 (𝑥 2 (𝑥 − 7)3 )
√3𝑥 2 −1
b. ln ((𝑥+2)𝑥 5 )
c. log 2 (
3
5𝑥 2 √1−𝑥
4(𝑥+1)2
)
2. Condense each expression to a single logarithm.
1
a. log 𝑎 𝑥 + 6 log 𝑎 (𝑥 − 8) + log 𝑎 (𝑥 2 + 6)
2
b. −4 ln 4 + ln(𝑥 + 3) − 6ln⁡(𝑥 + 3)
Let’s talk about how to use your calculator to find the value of not-sonice logarithms.
3. Use your calculator to approximate to 3 decimal places
a. log 9 18
b. log 𝜋 100
4. Use a calculator to solve for x.
a. 5𝑥+1 = 39
2
b. 3𝑥 = 13
Homework 6.5:
p. 457: #13-85 EOO, 97