Question

Simplify log5 (x+2) - log5 10= log 5 100

a.108
b.8
c.998
d.1000

Answer 1

I think you mean solve for x rather than simplify?

Answer 2

do you know the various log rules?

Answer 3

Yes, i do but how do i apply it to this?

Answer 4

start with the left-hand-side

Answer 5

use the rule:\[\log_a(p)-\log_a(q)=\log_a(\frac{p}{q})\]

Answer 6

but how does this formula pertain to the question?

Answer 7

its asking you to find the value of x in this equation. so you need to first simplify the left-hand-side

Answer 8

you have this on the left-hand-side:\[\log_5(x+2) - \log_5(10)\]use the rule I gave above to first simplify this expression

Answer 9

thank you so muc, i have a question in order to simplify it what do i do with the log5 10 ?

Answer 10

use the rule I gave above, i.e use:\[\log_a(p)-\log_a(q)=\log_a(\frac{p}{q})\]in your case p=x+2 and q=10

Answer 11

and 'a' is the base of the log which is 5 in your case

Answer 12

Ohhhhh, the answer i have come up with is 108 Is that correct?

Answer 13

no

Answer 14

tell me what you got when you simplified the left-hand-side please

Answer 15

I give up, Thank You so much for your help though!

Answer 16

I take you through it step-by-step if you want to learn?

Answer 17

*I can ...

Answer 18

okay sure then

Answer 19

ok, so you are given:\[log_5(x+2) - \log_5(10)= \log_5(100)\]use the rule I gave above, we can simplify the left-hand-side as follows:\[\log_5(\frac{x+2}{10})=\log_5(100)\]

Answer 20

do you follow so far?

Answer 21

so i jsut plug the numbers in then?

Answer 22

yes

Answer 23

no - no need to plug in any numbers

Answer 24

next step is to notice that both sides are logs of something to base 5

Answer 25

so i cancel them out? or add them up?

Answer 26

therefore the "something" within the logs must be equal

Answer 27

yes.

Answer 28

therefore:\[\frac{x+2}{10}=100\]

Answer 29

do you know how to find x from here?

Answer 30

obviously, lol okay simplify

Answer 31

YES THANK YOU SO MUCH!

Answer 32

yw

Answer 33

you are a mathj genius!

Answer 34

:)

Answer 35

the answer is c, 998 right.

Answer 36

correct - well done! :)

Answer 37

*claps* Thank You.

Answer 38

:D