LOGARITHM HELP

Question

Write as the sum or difference of logarithms. 1. log_6((2x^3)/3) 2. ln (x^2 y) 3. log_7 (sqrt xy^3) HELP!!!

Answer 1

First remember the basic rules:

 

log_n ab = log_n a + log_n b

log_n a/b = log_n a - log_n b

log_n a^b = b log_n a 

 

These rules apply no matter what the base of the logarithm is.

 

1. log₆ ((2x³)/3) =

log₆ (2x³) - log₆ 3 =

log₆ 2 + log₆ x³ - log₆ 3 =

log₆ 2 - 3 log₆ x - log₆ 3

 

2. ln (x² y) = 

ln x² + ln y =

2 ln x + ln y

 

3. log₇ (sqrt xy³)

 

It's not clear if you mean sqrt (xy³) or sqrt (x) y³.  Let's guess that you meant sqrt (xy³).

 

So that's log₇ (xy³)^1/2 = 

1/2 log₇ (xy³) =

1/2 (log₇ x + log₇ (y³) =

1/2 (log₇ x + 3 log₇ y) = 

(log₇ x + 3 log₇ y) / 2