The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Core 3 - Logs

if ln( x^6 y) - 2 ln (xy) + ln (3xy^2) = 2

prove that y = kx^n where k and n are constants

find the exact values of y = kx ^n

1) i've separated the equation:

ln x^6 + lny - 2(lnx + lny) + ln 3x + lny^2 =2

where do I go from here?
Original post by Custardcream000
if ln( x^6 y) - 2 ln (xy) + ln (3xy^2) = 2

prove that y = kx^n where k and n are constants

find the exact values of y = kx ^n

1) i've separated the equation:

ln x^6 + lny - 2(lnx + lny) + ln 3x + lny^2 =2

where do I go from here?


No need to separate them. Get them all under the same logarithm instead.
Original post by Custardcream000
if ln( x^6 y) - 2 ln (xy) + ln (3xy^2) = 2

prove that y = kx^n where k and n are constants

find the exact values of y = kx ^n

1) i've separated the equation:

ln x^6 + lny - 2(lnx + lny) + ln 3x + lny^2 =2

where do I go from here?


I think you've headed in the wrong direction to start with... kind of. Doesn't mean you can't go on from there, but you've kind of made... 1 more step... I dunno. Maybe that doesn't matter :tongue:

Think about somehow combining the logs.
Original post by RDKGames
No need to separate them. Get them all under the same logarithm instead.


so do you get ln( x^6y 3xy^2 / x^2 y^2 ) =2

ln(3x^5y)=2

where do i go from here??
Original post by Custardcream000
so do you get ln( x^6y 3xy^2 / x^2 y^2 ) =2

ln(3x^5y)=2

where do i go from here??


ln is log with base e. So anti-log both sides.
Original post by RDKGames
ln is log with base e. So anti-log both sides.


3x^5 y = e^ 2

y= e^2 / 3x^5
Original post by Custardcream000
3x^5 y = e^ 2

y= e^2 / 3x^5


Yep. You can take the x out of the denominator as 1x=x−1\displaystyle \frac{1}{x}=x^{-1}
Original post by RDKGames
Yep. You can take the x out of the denominator as 1x=x−1\frac{1}{x}=x^{-1}


so y = (e^2/3) x^-5
Original post by Custardcream000
so y = (e^2/3) x^-5


Yep.
Original post by RDKGames
Yep.


thanks for your help

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you