Question

Please help!!
log8(x+2)-log8(x-1)=2/3
Since the base is common I set log8 (x+2)(x-1)=2/3. CAn anyone let me know if this is correct and help me find the solution, please. Thanks in advanced.

Answer 1

almost - the correct rule to use here would be:\[\log_ap-\log_aq=\log_a(\frac{p}{q})\]

Answer 2

you can find some basic log rules here to help you: http://www.purplemath.com/modules/logrules.htm

Answer 3

so that would be log8 x+2/x-1=2/3??

Answer 4

yes

Answer 5

i have the rules....i'm just getting stumped on the steps. I need a little guidance.

Answer 6

ok - np

Answer 7

so do you know what the next step should be?

Answer 8

remember, if:\[\log_ap=n\implies p=a^n\]

Answer 9

2/3(x-1)=(x+2)??

Answer 10

no - look carefully at the rule I just posted above and try it again

Answer 11

in your case:\[a=8\]\[p=\frac{x+2}{x-1}\]\[n=\frac{2}{3}\]

Answer 12

ok.....working it out now...hold on a sec. thanks

Answer 13

np - take your time :)

Answer 14

i got log8 x+2/x-1=2/3

Answer 15

i now multiply 2/3 by both sides to get rid of teh fraction correct? or is it the inverse 3/2

Answer 16

no, after your first simplification to:\[\log_8(\frac{x+2}{x-1})=\frac{2}{3}\]you need to use the second rule I gave you, i.e. if:\[\log_ap=n\]then this implies:\[p=a^n\]

Answer 17

(x+2/x-1)=8^2/3

Answer 18

correct

Answer 19

now try and simplify the right-hand-side, i.e. simplify:\[8^{\frac{2}{3}}\]

Answer 20

this can be written as:\[8^{\frac{2}{3}}=(8^{\frac{1}{3}})^2\]

Answer 21

and \(8^{\frac{1}{3}}\) means the cube-root of 8

Answer 22

not (2^3)^2/3

Answer 23

where did you get that from?

Answer 24

lol....my brain is so mixed up...sorry

Answer 25

:)

Answer 26

the last correct step we got to was:\[\frac{x+2}{x-1}=8^{\frac{2}{3}}\]so then I asked you to first simplify the right-hand-side of this equation, i.e. simplify:\[8^{\frac{2}{3}}=(8^{\frac{1}{3}})^2\]

Answer 27

where \(8^{\frac{1}{3}}\) means the cube-root of 8

Answer 28

do you know what the cube-root of 8 is?

Answer 29

2

Answer 30

good, so we can write:\[8^{\frac{2}{3}}=(8^{\frac{1}{3}})^2=(2)^2=?\]

Answer 31

4

Answer 32

great, so now going back to our last equation we get:\[\frac{x+2}{x-1}=8^{\frac{2}{3}}=4\]next step is to multiply both sides by (x-1)

Answer 33

answer is x=2

Answer 34

correct

Answer 35

yes...site froze

Answer 36

i worked it out...i wish i had an answer sheet

Answer 37

ok - thats even better!
these types of problems just need plenty of practice - you'll be a pro pretty soon!

Answer 38

thank you soo much.i hope so

Answer 39

yw