Question

express as single log...:-
4 log x - 6 log (x+2)

Answer 1

@hartnn @ganeshie8

Answer 2

@Luigi0210 ?

Answer 3

use below property to start with :
\[\large a \log b = \log b^a\]

Answer 4

apply that for both the terms in your expression, what do u get ?

Answer 5

logx^4 and log(x+2)^6

Answer 6

wait i knw the property

Answer 7

so it is log x ^ 4/(6)......... but wat about base that are different?

Answer 8

\[\Large \log_{}a-\log_{}b=\log(\frac{a}{b} )\]

Answer 9

Excellent ! so we have :

\[\large 4 \log x - 6 \log (x+2)\]

\[ \large = \log x^4 -\log (x+2)^6\]

Answer 10

yea........i saw and i typed the property up there.......but different bases so wat next?

Answer 11

we cant do log x ^ (4/6)

Answer 12

actually x and (x+2) are NOT bases here...
there is no explicit base given here - you can assume the base is 10

Answer 13

Think of the x^4 and the (x+2)^6 work as a and b as I've stated before and what @ganeshie8 there's no base given (it's usually just 10 in this case)

Answer 14

like below :

\[\large 4 \log_{10} x - 6 \log_{10} (x+2)\]

\[ \large = \log_{10} x^4 -\log_{10} (x+2)^6\]

Answer 15

ohh ok........ so lets say..... log 10 ^ (x^4/ (x+2)^6)....right?

Answer 16

Looks perfect !

Answer 17

ok.......it will take me time to expand the (x+2)^6

Answer 18

I think you can just leave it just like that, does your work say to expand?

Answer 19

don't even thinka bout it

Answer 20

I'd drop the base 10 in the final answer though as it was not in the original problem.

Answer 21

\[ \large = \log\left( \dfrac{x^4}{ (x+2)^6}\right)\]


END of story.

Answer 22

k so my options are :-

a) 24 log x/x+2
b) log x^4 (x+2)^6
c)log x (x+2)^24
d) none of the above....

Answer 23

it is (d).........i think

Answer 24

Remember \[\large a \log b = \log b^a\]? Yu'll need to use it again

Answer 25

@doulikepiecauseidont ........... Yes Sir...

Answer 26

@ganeshie8 .........yea so i think it is option (d)........

Answer 27

i hesitate to tick NOTA usually... could you take a screenshot of question/options and attach if possible ?

Answer 28

yes wait.....give me a second....

Answer 29

is it viewable????

Answer 30

ty :) You're right ! it has to be NOTA

Answer 31

@ganeshie8 thanks a lot for the help professor....lol......thanks to u too bro @doulikepiecauseidont

Answer 32

\[\large \log\left( \dfrac{x^4}{ (x+2)^6}\right)=\log\left( \dfrac{x^2}{ (x+2)^3}\right)^{2}=2\log\left( \dfrac{x^2}{ (x+2)^3}\right)\]

I was thinking it was A before but it would be this in case you were wondering..

Answer 33

np (: