Question

Write the following in expanded form using logarithmic properties
log5 x^3y
----
z^4

Answer 1

can someone please help me

Answer 2

The problem is


\[\Large \log_{5} \left(\frac{x^3y}{z^4}\right)\]


right?

Answer 3

yes

Answer 4

ok we'll need to use these rules given here

http://www.purplemath.com/modules/logrules.htm

Answer 5

do those rules look familiar?

Answer 6

yes

Answer 7

what's the first step? any ideas?

Answer 8

would you do log5 X^3 +log5 Y - log5 Z^4

Answer 9

it just looks wrong for some reason though

Answer 10

you're very close to the final answer

Answer 11

where did i go wrong on it? can you please explain

Answer 12

Here's the full step by step picture (you'll see that you're on the right track)

Answer 13

Use the log rules given on this page



http://www.purplemath.com/modules/logrules.htm



to get



\[\Large \log_{5} \left(\frac{x^3y}{z^4}\right)\]



\[\Large \log_{5} \left(x^3y\right)-\log_{5} \left(z^4\right) \ ... \ \text{Use rule 2}\]



\[\Large \log_{5} \left(x^3\right)+\log_{5} \left(y\right)-\log_{5} \left(z^4\right) \ ... \ \text{Use rule 1}\]



\[\Large 3\log_{5} \left(x\right)+\log_{5} \left(y\right)-4\log_{5} \left(z\right) \ ... \ \text{Use rule 3}\]

Answer 14

So you just needed to use rule 3 to pull those exponents down

Answer 15

ohh okay that makes sense
thank you

Answer 16

you're welcome

Answer 17

one more quick question for this question log7p^6q^3r^1/4

Answer 18

would it be like 6log7p + 3log7q + 1/4 log7r

Answer 19

I'm assuming the original expression is

\[\Large \log_{7} \left(p^{6}q^{3}r^{1/4}\right)\]

Answer 20

yes

Answer 21

Then

\[\Large 6\log_{7} \left(p\right)+3\log_{7} \left(q\right)+\frac{1}{4}\log_{7} \left(r\right)\]

is the correct expansion

Answer 22

thank you :)

Answer 23

you're welcome