Form 6 Maths T logarithms!

[michiyo84]

sorry but i dont really know where should i post about this but i need an urgent reply. thanks!

how do we solve this simultaneous equations??

log(to base 9)xy = 1/2
log(to base 3)xlog(to base 3)y = -2
thats the question.....somehow i get this during my calculations : xy = 3
x+y = 1/9

the answers are x = 9 or 1/3
y = 1/3 or 9

i dont know the way to get the answers! help!

[Cactus]

sorry but i dont really know where should i post about this but i need an urgent reply. thanks!

how do we solve this simultaneous equations??

log(to base 9)xy = 1/2
log(to base 3)xlog(to base 3)y = -2
thats the question.....somehow i get this during my calculations : xy = 3
x+y = 1/9

the answers are x = 9 or 1/3
y = 1/3 or 9

i dont know the way to get the answers! help!

First, I suggest that you use more brackets when you try to express:

[log(to base 3)x][log(to base 3)y] = -2

log9 xy = 0.5 (given)

Hence, log3 xy = 1

log3 x + log3 y = 1 ------ (1)

Also given [log(to base 3)x][log(to base 3)y] = -2 ----- (2)

Let a = log3 x, b = log3 y and substitute into equations 1 and 2.

Solve for a and b, and get the corresponding values of x and y.

[michiyo84]

THANK YOU SO MUCH!!!!!!!!!!!
I got the answers at last!!! It took me like almost a day to get the answers. THANKS!!! :D :))