Question

Simplify the expression attached and write it as a single logarithm..

***still confused on this topic... pls help? :)

Answer 1

answer choices A,B,C,D from top to bottom :)

Answer 2

Move all the exponents up:

\((x+4)^{-3}\)

\((x-7)^{2}\)

\((x-2)^{5}\)

\((x^{2})^{-1}\)

Notice how I deliberately left everything outside as ADDITION. This allows us just to bring everything inside without concern for numerator or denominator. We can figure all that out later.

Answer 3

im confused.. so how can i apply that with my expression?

Answer 4

Confused with what? \(-3\log(x+4) = \log\left[\left(x+4\right)^{-3}\right]\) Correct?

Answer 5

im not quite sure what we are working on now.. I'm like uber confused.. are we doing my problem? or an example? :/ sorry I'm a bit confused :(

Answer 6

Your problem statement begins \(-3\log(x+4)\), doesn't it? Or am I looking at some other picture?

Answer 7

yup iy does :) so i get log[(x+4)^−3] from that part?

Answer 8

Very good. Now the (x-7) part?

Answer 9

2log(x-7) = log(x-7)^2 ??

Answer 10

Good, now the x-2...

Answer 11

5log(x-2)=log(x-2)^5 ??

Answer 12

One more. You're on a roll!

Answer 13

lol thanks haha :P but i don't get this one... it looks different.. :/

-logx^2...

Answer 14

but heres my take on it..

log(x^2)^-1 ??

Answer 15

Take the negative (-1) inside, just like the other coefficients ==> exponents.

Answer 16

was what i got right?? or no?

Answer 17

or is it log(x)^-2 ?

Answer 18

There it is. They are now all connected by addition. Use this guy and bring them all together. log(a) + log(b) = log(a*b)

Answer 19

sorry my computer crashed... one sec :/

Answer 20

log[(x+4)^−3]+ log(x-2)^5+log(x-7)^2 + log(x)^-2=answer B right? :)

Answer 21

use the rule described above to go from

log[(x+4)^−3]+ log(x-2)^5+log(x-7)^2 + log(x)^-2

to

log[ (x+4)^−3*(x-2)^5*(x-7)^2*(x)^-2 ]

Answer 22

kk I'm seeing that :) but how can i simplify it even further?

Answer 23

(x+4)^−3 is really 1/[ (x+4)^3 ]

Answer 24

same idea applies to (x)^-2

Answer 25

ok so i get 1/x^-2 ?

Answer 26

yep

Answer 27

so put that all together

Answer 28

so i get answer C right?? :)

Answer 29

sorry i meant answer D :) is it answer D then? :)

Answer 30

@jim_thompson5910 :)

Answer 31

yes it is D

Answer 32

kk great!!! thx :)