Solve the simultaneous equations to 3 significant figure 3^x-4^y=5, 3^x+1 +4^y=23?
回答 (3)
2017-01-17 9:51 pm
3^(x) - 4^(y) = 5 …… [1]
3^(x+1) +4^(y) = 23 …… [2]
[1] * 3 :
3^(x + 1) - 3 * 4^(y) = 15 …… [3]
[2] - [3] :
4^(y) + 3 * 4^(y) = 8
4^(y) * (1 + 3) = 8
4^(y) = 2 …… [4]
4^(y) = 4^(1/2)
y = 1/2
Substitute [4] into [1] :
3^(x) - 2 = 5
3^(x) = 7
log[3^(x)] = log(7)
x log(3) = log(7)
x = log(7)/log(3)
Hence, x = log(7)/log(3), y = 1/2
3^(x+1) +4^(y) = 23 …… [2]
[1] * 3 :
3^(x + 1) - 3 * 4^(y) = 15 …… [3]
[2] - [3] :
4^(y) + 3 * 4^(y) = 8
4^(y) * (1 + 3) = 8
4^(y) = 2 …… [4]
4^(y) = 4^(1/2)
y = 1/2
Substitute [4] into [1] :
3^(x) - 2 = 5
3^(x) = 7
log[3^(x)] = log(7)
x log(3) = log(7)
x = log(7)/log(3)
Hence, x = log(7)/log(3), y = 1/2
2017-01-17 9:44 pm
3^x-4^y=5 ...(1)
3^x+1 +4^y=23 ...(2)
Add (1) and (2)
3^x + 3^(x +1) = 28
3^x + 3.3^x = 28
3^x(1+3) = 28
3^x = 28/4 = 7
Take log with base 3 both sides
x = log ₃ (7) = 1.771
I think solving for y is trivial now
3^x+1 +4^y=23 ...(2)
Add (1) and (2)
3^x + 3^(x +1) = 28
3^x + 3.3^x = 28
3^x(1+3) = 28
3^x = 28/4 = 7
Take log with base 3 both sides
x = log ₃ (7) = 1.771
I think solving for y is trivial now
2017-01-17 9:45 pm
3^x -4^y = 5
3^(x+1)+4^y = 23
add:
3^x+ 3^(x+1) = 28
3^x + 3^x * 3 = 28
3^x(1+3) = 28
4* 3^x = 28
3^x = 7
x log(3) = log(7)
x = log(7)/log(3)
x= 1.771
3^x-4^y = 5
3^1.771 - 4^y = 5
4^y = 3^1.771 -5
4^y = 1.998
y log(4) = log(1.998)
y = log(1.998)/log(4)
y=0.499
3^(x+1)+4^y = 23
add:
3^x+ 3^(x+1) = 28
3^x + 3^x * 3 = 28
3^x(1+3) = 28
4* 3^x = 28
3^x = 7
x log(3) = log(7)
x = log(7)/log(3)
x= 1.771
3^x-4^y = 5
3^1.771 - 4^y = 5
4^y = 3^1.771 -5
4^y = 1.998
y log(4) = log(1.998)
y = log(1.998)/log(4)
y=0.499
收錄日期: 2021-04-18 15:58:09
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