Jawapan

2016-06-16T02:22:56+08:00
 9^{x} = m , ㏒ 3^{y} = n
 x = 9^{m} , y = 3^{n}
x =  3^{2m}

a) xy dan  \frac{x}{y}
    xy = ( 3^{2m} ) (  3^{n} )
             3^{2m+n}

    \frac{x}{y}  \frac{ 3^{2m} }{ 3^{n} }
                                        3^{2m-n}

b) xy = 243
     3^{2m+n} =  3^{5}     2m+n = 5     n = 5-2m ___first equation        [tex] \frac{x}{y} = 27 /  3^{2m-n} = 27     3^{2m-n} =  3^{3}
    2m-n = 3
    2m-3 = n ___2nd equation
  
1st equation = 2nd equation
5-2m = 2m-3
2m+2m = 5+3
4m = 8
m = 2

m=2 in 1st
n = 5-2m
   = 5-2(2)
   =1

m=2 in 2nd equation
n = 2m-3
   = 2(2)-3
   = 1



y = px^{n} - 24

y = -8 apabila x=2
-8 = p(2)^{n} - 24
16 = 2p^{n}
p^{n} = 8
2³ = 8
p=2 , n=3

y=104 apabila x=4
104 = p(4)^{n} - 24
128 = 4p^{n}
p^{n} = 32
2^{5} = 32
p=2 , n=5