exponenciální rovnice
a) 2^x+1 + 2^x-1 + 2^x+3 = 21/8
b) 7 * 4^-x+2 = 3 * 4^-x+3 - 5
c) 4/5 * 5^-1 - 25^x + 20 * 25^x-1 = 0
d) 3^x * (1/2)^x + 3^x+1 * (1/2)^x+1 = 5/3
e) 2^2x * 5^x - 2^2x-1 * 5^x+1 = -600
b) 7 * 4^-x+2 = 3 * 4^-x+3 - 5
c) 4/5 * 5^-1 - 25^x + 20 * 25^x-1 = 0
d) 3^x * (1/2)^x + 3^x+1 * (1/2)^x+1 = 5/3
e) 2^2x * 5^x - 2^2x-1 * 5^x+1 = -600
Odpovědi
Diskuze
2^(x+1) + 2^(x-1) + 2^(x+3) = 21/8
2^x*2^1+ 2^x*2^-1 + 2^x*2^3 = 21/8
2^x*(2+1/2) + 2^x*8 = 21/8
2^x*(2+1/2) + 2^x*8 = 21/8
2^x*(2+1/2+8) = 21/8
2^x*(10+1/2) = 21/8
2^x*(21/2) = 21/8
2^x = 2/8
2^x = 1/4
x = log2 (1/4)
x = log2 (1)-log2 (4)
x = log2 (1)-log2 (4)
x = 0-2
x=-2
3^x*(1/2)^x + 3^(x+1)*(1/2)^(x+1) = 5/3
3^x*(1/2)^x + 3^x*3*(1/2)^x*(1/2) = 5/3
3^x*(1/2)^x*(1 + 3/2) = 5/3
3^x*(1/2)^x*(5/2) = 5/3
3^x*(1/2)^x = 2/3
(3/2)^x = 2/3
=> x = -1