Question

log question!
Log[2] (x+3)+log[2] (x+5)=1
answer: -2
I've tried this problem and I keep getting stuck!
I know I need to start with the FOIL property, but after that, I keep getting mixed up. Can someone shed some light please? and show me how to get -2? D: Thank you!

Answer 1

\[log_2 (x+3)+log_2 (x+5)=1~~~~?\]

Answer 2

precisely.

Answer 3

Well first use \[\log_a(b)=\frac{\log_c(b)}{\log_c(a)}\]
Did you use this?

Answer 4

\[log_ax=y,\ a^y=x\]\[log_2(x+3)(x+5)=1,\ 2^1=(x+3)(x+5)\]

Answer 5

You will get\[\frac{\log (x+3)}{\log 2}+\frac{\log (x+5)}{\log 2}=1\]
Then
\[\log ((x+3) (x+5))=\log 2\]

Answer 6

Then (x+3) (x+5)=2

Answer 7

Expand and complete the square
\[x^2+8 x+15=2\]
\[(x+4)^2=3\]

Answer 8

...Or you can just solve as a quadratic by moving the 2 to the LHS (Left Hand Side).

Answer 9

Both cases will do, but I find completing the square is faster

Answer 10

@.Sam. Where did you get ans=-2?

Answer 11

-2 is in the back of the book. It said that was the answer, but I am not getting it. I have done the steps that have been shown to me. :O

Answer 12

I don't think you can get -2, the answer should be
\[x=\sqrt{3}-4 ~~ or ~~x=-\sqrt{3}-4\]

Answer 13

Did you checked it correctly?

Answer 14

Look at your question to double check if you made a typo when writing out the question.

Answer 15

Hey @stamp I believe x=-2 is never possible ... If you simply substitute -2 in the L.H.S you won't be getting 1...

Answer 16

I have numerously checked the answer. But our teacher said that this text book we have has some mistakes (even in the examples) so maybe this is why we're getting stuck.

Answer 17

@saloniiigupta95 dun dundunnnnn

Answer 18

Sorry but Didn't get what you mean...

Answer 19

Use the property...

(x in the base of log)