Question

log(p+q)(p-q) = -1
log(p+q)log(p^2-q^2) = ?

option: a)2 b)1 c) -1 d) 0

Answer 1

cud anybody give me the full solution. ?

Answer 2

umm I don't know if this is correct:

\[\log(p+q)\log(p^2-q^2) =?\]
\[\log(p+q)\log(p-q) = -1\]


so first equation is turned into:
\[\log(p+q)\log((p+q)(p-q)) = ?\]

Answer 3

since \[\log(p+q)(p-q) = -1\]

so \[\log(p+q) -1 =0\]

Answer 4

log(p^2-q^2) = log(p+q)(p-q) = -1

but i cant see a way to find what log(p+q) is.

Answer 5

@welshfella that's in my last reply

Answer 6

log(p+q) = 1

Answer 7

so since log(p+q) = 1
it will be:
\[\log(p+q)\log(p^2-q^2) = 0\]

Answer 8

i cant see your logic there - I'm not saying you are wrong

Answer 9

I mean to say that since log(p^2-q^2) = -1

log(p+q)log(p^2-q^2) = will be

log(p+q) -1 = 0

so log(p+q) = 1

Answer 10

if log ( p + q) = 1
log(p+q)log(p^-q^2) = 1 * -1 = -1 not 0

Answer 11

oh yes my bad I was subtracting
then yes it would be -1

Answer 12

@nopen it looked like you said:
\[\log(a \cdot b)=\log(a) \cdot \log(b) \text{ thisn't a log property though }\]

Answer 13

can the asker post the screenshot of the question?

Answer 14

but isn't it

log(a*b) = log(a) + log(b)?

Answer 15

yes that is true

Answer 16

that is the product rule for log

Answer 17

I think the answer is zero
let p+q = 1 and p-q = 0.1
then log(p+ q)(p - q) = log 0.1 = -1
which fits in with log(p+q) + log(p-q) = 0 + (-1) = -1 because the log of 1 is 0

so when we multiply by log(p+q) we are multiplying by 0

so the log(p+q)log(p^2 - q^2) = 0*-1 = 0

Answer 18

yeah its d

Answer 19

well I don't think this can be answered with the info given
here is a counterexample to not being zero for all p and q that satisfy the condition log(p^2-q^2)=-1
\[\text{ Let } p+q=10^{-2} \text{ and } p-q=10 \\ \text{ so } p^2-q^2=10^{-1} \\ \text{ so } \log((p+q)(p-q))=-1 \\ \text{ but } \\ \log(p+q)\log(p^2-q^2)=(-2)(-1)=2\]

Answer 20

yes - that is correct - we need more info to get a definitive answer.

Answer 21

a picture would be nice as suggested by @hartnn

Answer 22

yes

Answer 23

thank you @nopen

Answer 24

but we cant assume log(p+q)log(p+q)(p-q)=0, as this condition is not given.
if log(p+q)(-1)=? that too is in multiplication.

Answer 25

\[\text{ Let } p+q=10^{A} \text{ then } p-q=10^{-1-A} \\ \text{ Since we need } \log[(p+q)(p-q)]=-1 \\ \text{ Verify our let part: } \\ \log[(10^{A})(10^{-1-A})]=\log[10^{A+(-1-A)}[=\log(10^{-1})=-1 \log(10)=-1(1)=-1 \\ \text{ Verified! } \\ \log(p+q)=\log(10^{A})=A \log(10)=A(1)=A \\ \log(p+q)\log(p^2-q^2)=A(-1)=-A\]
A can be any real number

Answer 26

and what wud be the answer in this case , 1 or 2?

Answer 27

no way to tell

Answer 28

Not enough info is given to apply one of the choices

Answer 29

I wonder if they mean (p+q) to be the base ...
if so...
the problem really is:
\[\log_{p+q}(p-q)=-1\]
so we have
\[(p+q)^{-1}=p-q\]

and we are trying to find:
\[\log_{p+q}((p-q)(p+q)\]
using product rule we have
\[\log_{p+q}(p-q)+\log_{p+q}(p+q)\]
\[\log_{p+q}((p+q)^{-1})+1\]
using power rule
(-1)+1=0
now this is all assuming p+q is in the interval (0,1) union (1,infty)

Answer 30

waooo , Great ... thanku @freckles

Answer 31

no sorry the question doesn't make sense lol
because they have more than one log in the thingy we are supposedly suppose to find

Answer 32

but it seems good

Answer 33

we are not given with any base , so we have to identify by ourself that the base is given or not

Answer 34

there is seriously not enough information to answer this question the way it is written
I have been trying to find other ways to possibly interpret the problem but i do not see a way to interpret the problem really that will lead to one of the answers but anyway I interpret it like the above I have leave something out

Answer 35

that is not ryt

Answer 36

what are you talking about?

Answer 37

the answer?

Answer 38

I didn't give an answer to your problem

Answer 39

the above way that you have used to solve the question

Answer 40

taking base p+q

Answer 41

I made up a question that could have a answer that is one of your choices
because the question you have could give us any of the choices (being that there is not enough information)

Answer 42

fine

Answer 43

answer is that, the question doesnt make any sense,. lol

Answer 44

lol
if p+q is the base, then this is a really simple problem,

log_(p+q) of p-q = -1

log_(p+q) (p^2-q^2)

= log_(p+q) of (p-q)(p+q)

=log_(p+q) of p-q + log_(p+q) of p+q

= -1+1=0