F.4 既數學 唔識做幾題 請師兄師姐幫手

1) 5(3^x)-7(3^x-1)=648
5(3^x)-7(3^x/3)=648
15(3^x)-7(3^x)=1944
8(3^x) =1944
3^x = 243
3^x = 3^5
x = 5

2) 16(3^x) -9(4^x) = 0
16(3^x) = 9(4^x)
3^x/4^x = 9/16
(3/4)^x = 3^2/4^2
(3/4)^x = 3^2/4^2
(3/4)^x = (3/4)^2
x = 2

3) 4^x+1 -3^y =7 ----- L1
3(4^x) + 2(3^y) =30 -----L2
4(4^x )- 3^y = 7 ----- L3
3 (4^x) + 2(3^y) =30 -----L4
Multiply L3 by 3 and multiply L4 by 4
12(4^x ) - 3(3^y) = 21 ----- L5
12 (4^x) + 8(3^y) = 120 -----L6
L6 minus L5
11(3^y) = 99
3^y = 99/11 = 9 = 3^2
y = 2
Substitute y = 2 into L3
12(4^x) - 3(9) = 21
12(4^x) = 27+21 = 48
4^x = 48/12 = 4 = 4^1
x = 1

x = 1 and y = 2


4) 2log9 <---個base係x 然後 減4 = 0
2 log(x)9 – 4 = 0
2 log(x)9 = 4
log(x)9 = 4/2 = 2
x^2 = 9
x = 3

5) log (3x-1) +log x =1
log x(3x-1) =1og 10
x(3x – 1) = 10
3x^2 –x – 10 = 0
(3x + 5)(x – 2) = 0
x = -5/3 or x = 2