Properties of Logarithms

Section 3.3
14 - 18


Question 14

log_3 (5/7) = log_3 (5) - log_3 (7)

Question 16

log_3 (175)

I know that 25 • 7 = 175.

log_3 (25) + log_3 (7)

Let 25 = 5^2.

log_3 (5^2) + log_3 (7)

2•log_3(5) + log_3 (7)

Question 18

log_3 (45/49)

Let 45 = 9•5

Let 49 = 7^2

log_3 (9•5) + log_3 (7^2)

log_3 (9) + log_3 (5) + 2•log_3 (7)

Let 9 = 3^2

log_3 (3^2) + log_3 (5) + 2•log_3 (7)

2•log_3 (3) + log_3 (5) + 2•log_3 (7)

I don't think 2•log_3 (3) is part of the answer for question 18.

You say?

 

correct

yes it is part of the answer for 18, and at the end you can change to base 10 if you want:

 

Ok. Looks good.