Question

Product of logarithms question
question below

Answer 1

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms.
\(\log_2(\dfrac{x^9y^5}{8})\)

\(9\log_2x-5\log_2y-\log_28\)
\(9\log_2x+5\log_2y-\log_28\)
\((9\log_2x)(5\log_2y)-\log_28\)
\(9\log_2x+5\log_2y+\log_28\leftarrow I~believe~it~is~this~one\ but\ I'm\ not\ sure\)

Answer 2

@zepdrix

Answer 3

\[\Large\rm \log(ab)=\log(a)+\log(b)\]\[\Large\rm \log\left(\frac{a}{b}\right)=\log(a)-\log(b)\]Here are two of the rules we need.

Answer 4

And so you're thinking it's the last option? :o

Answer 5

i think so but im not sure

Answer 6

See how we're dividing by the 8?
We would apply the difference rule to take him out of the bunch.

Answer 7

So we should end up with a -log(8) at the end.

Answer 8

ok so now i am thinking is is the third one

Answer 9

It is `definitely` not the third one...
See how they're multiplying two logs together?

We don't have a rule that would result in that happening.

Answer 10

ugh i am so frustrated with this my lessons dont explain anything and they dont even give us an example like this

Answer 11

@amistre64

Answer 12

@phi

Answer 13

are you doing this one
\[ \log_2\left(\dfrac{x^9y^5}{8}\right) \]?

Answer 14

yes

Answer 15

you do these problems in small steps.
for the moment, let's call the "top" A , and write the problem as
\[ \log_2\left(\dfrac{A}{8}\right) \]

do you see we have A divided by 8 "inside" the log ?

Answer 16

yes

Answer 17

do you know how to re-write this using the rule
\[ \log(A/B)= \log(A) - \log(B) \]
?

Answer 18

(It will still be log base 2 )

Answer 19

9 log base 2 x +? 5 log base 2 y - log bae 2 8?