Question

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1:

log(x) + log(x^2-49) - log12 - log(x+7)

Answer 1

So far I have hte following: log((x)*(x^2-49))/....

Answer 2

Above all, I'm not sure how to simplify the log12

Answer 3

Or rather, how to find the denom. in general. Any ideas?

Answer 4

Is it just (12/(x+7)?

Answer 5

you know \(\log a+\log b = \log ab \\ also,\log a-\log b = \log a/b \)

Answer 6

Yes, I'm aware of all that.

Answer 7

Factorise (x^2 - 49) (hint: part of this can then be cancelled out)

Answer 8

If you're aware, then use it. Put it within one log and simplify.

Answer 9

Where are you getting (x^2 - 49) from, by the way?

Answer 10

log(x^2-49)

Answer 11

so
log(x) + log(x^2-49) - log12 - log(x+7)
= log(x* (x^2-9) /[ 12 * (x+7) ] )
got this ?

Answer 12

Oh...nevermind, wrong part of the problem..sorry...

Answer 13

Yeah...that's what I entered (i.e. the site's saying it's wrong)

Answer 14

Or no...I entered 12/(x+7) as the denom.

Answer 15

Since in the original expression, you're subtracting (x+7) from log12

Answer 16

that is incorrect, u got how ?
and you can simplify
x^2-49 = x^2-7^2 =??

Answer 17

- log12 - log(x+7) = - ( log12 log(x+7)) = -(log [12*(x+7)])

Answer 18

Basically in a log equation, whatever has a + sign goes on the top (numerator) and whatever has a - goes on the bottom (denominator)

As long as they are of the same base and coefficient

Answer 19

Okay...but in this one, there are two logs preceded by -, so does that mean the denominator is a fraction?

Answer 20

no, \(\log a-\log b-\log c= \log (a/bc)\)

Answer 21

\(\log a-\log b-\log c=\log a -(\log b+\log c)= \log (a/bc)\)

Answer 22

got it ?

Answer 23

Yep. Thank you.

Answer 24

So the denom is (12x+84)?

Answer 25

keep it as 12(x+7)
because in numerator u get
x^2-49 = (x+7)(x-7)
so that u can cancel x+7

Answer 26

So the num. becomes (x*x-7)?

Answer 27

yeah and denominator = ?

Answer 28

12?

Answer 29

yes.

Answer 30

Do I need two sets of parentheses around the denom?

Answer 31

so u finally get
\(\log [x(x-7)/12]\)
got this ?

Answer 32

ohh....okay

Answer 33

Yes...thank you soo much!!

Answer 34

Have a good day/night hartnn and I appreciate all your help!!

Answer 35

you too :)
welcome ^_^