Question

log3(xy)^3-log3xy= 3log3????

Answer 1

I'm not sure I understand the equation. Is it\[\log_{3}{(xy)^3}-\log_{3}{(xy)}=3\log_{10}{(3)}?\]

Answer 2

yes

Answer 3

First of all, do you think we can simplify the left-hand-side? Perhaps using this property\[\log(a)-\log(b)=\log(\frac{a}{b})?\]

Answer 4

no, the 3log3 was my answer to the question

Answer 5

Well, the LHS of the expression is a function of x and y whilst the RHS is a constant. How can that be?

Answer 6

what is LHS?

Answer 7

left-hand-side

Answer 8

left hand side

Answer 9

I have never seen these problems in my life, I only started Logarithms today.

Answer 10

\[\log_{3}(xy)^3-\log_{3}(xy)=\log_{3}(x^3y^3)-\log_{3}(xy)=\log_{3}(\frac{x^3y^3}{xy})=?\]

Answer 11

log x2 y2?

Answer 12

base 3

Answer 13

That's correct.

Answer 14

and that cam be simplified to 2log3(xy) right??

Answer 15

Yep:\[\log_{3}{(x^2y^2)}=\log_{3}{(xy)^2}=2\log_{3}{(xy)}.\]

Answer 16

It's all about the properties...

Answer 17

thank you ms MIT