Properties of Logarithms

[nycmathguy]

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?

 

[MathLover1]

correct

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

 

[nycmathguy]

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.