我想問MATHS,,緊急20分!!!!thxxx

1. (5^x+1) = 100 + (5^x)
I think you are asking (5^(x+1)) = 100 + (5^x)
Let y = 5^x, then 5y = 100 + y
y = 25
so x = 2

2. (5^(x+1)) - 2(5^(x+1))=23
similarly let y = 5^(x+1), y-2y = 23, y= -23, so no solution
I think you have typed the wrong question

3. (2^(x+3)) + (2^x)=9/16
Let y = 2^x, 8y+y = 9/16
y = 1/16, so x = -4

4. (2^(2x+1))-6+(4^x)=0
Let y = 2^2x, 2y-6+y = 0
y = 2, so x = 1/2

5. (2^(3x-1))+15=(8^(x+1))
Let y = 2^3x, y/2+15 = 8y
y = 2, so x = 1/3

6. (25^(x+1))+5=126(5^x)
Let y = 5^x
25y^2 + 5 = 126y
25y^2 - 126y + 5 = 0
(25y-1)(y-5) = 0
y = 5 or y = 1/25
so x = 1 or -2

(a) (5^x+1) = 100 + (5^x)
1=100
x=infinity(無限大)

(b) (5^x+1) - 2(5^x+1)=23
-(5^x)-1=23
-5^x = 24
log(-1) + xlog5 = log24
x = (log5)/[log24 + log(-1)] (which is an imaginary number)

(c) (2^x+3) + (2^x)=9/16
2(2^x) = -39/16
2^x = -39/32
xlog2 = log(-1) + log39 - 5log2
x = [log(-1) + log39 - 5log2] / log2 (which is an imaginary number)

(d) (2^2x+1)-6+(4^x)=0
4^x+1-6+4^x = 0
2(4^x) = 5
log2 + xlog4 = log5
x = (log5 - log2)/2log2

(e) (2^3x-1)+15=(8^x+1)
2^3x-1 +15 = 2^3x+1
-14=1
x=infinity

(f) (25^x+1)+5=126(5^x)
5^2x + 1 + 5 = 126(5^x)
.......

可能係你寫錯, 又或者太艱深

(5^x+1) = 100 + (5^x)
1=100
no solution

(5^x+1) - 2(5^x+1)=23
5^x=-24
no solution

(2^x+3) + (2^x)=9/16
no solution

(2^2x+1)-6+(4^x)=0
x=(ln5-ln2)/ln4

(2^3x-1)+15=(8^x+1)
no solution

(25^x+1)+5=126(5^x)
5^2x-126(5^x)+6=0
5^x=63±開方15870
x=ln(63±開方15870)/ln 5