17.
c)
= [(1000 : 25 : 8 + 9 · 25) : 1] ·2¹ =
= (40 : 8 + 225) · 2 =
= (5 + 225) · 2 =
= 230 · 2 =
= 460
d)
= {[(144 + 25) : 13]² - 128 - 1} : 8 =
= [(169 : 13)² - 129] : 8 =
= (13² - 129) : 8 =
= (169 - 129) : 8 =
= 40 : 8 =
= 5
18.
a)
[tex]((2^{2} )^{x} )^{2} = 2^{2*x*2} = 2^{4x} \\2^{4x} =2^{8} \\4x=8\\x=2[/tex]
b)
[tex]((2*5)^{x} )^{5} *10*10 = (2^{4} )^{8} *(5^{4} )^{8} \\(2^{x} *5^{x} )^{5} *2^{2}*5^{2} = (2^{4} )^{8} *(5^{4} )^{8} \\2^{5x} *5^{5x} *2^{2}*5^{2} = 2^{32} *5^{32} \\2^{5x+2} *5^{5x+2} = 2^{32} *5^{32} \\5x+2=32\\5x=30\\x=6[/tex]
c)
[tex]5^{2(x+3)}= 5^{4x+2} \\2(x+3)=4x+2\\2x+6=4x+2\\4=2x\\x=2[/tex]
d)
x : 1 = 1
x = 1
e)
[tex]3^{5x} =3^{15} \\5x=15\\x=3[/tex]
f)
[tex]7^{4x} =7^{5*2^{2} }\\7^{4x} =7^{5*4 }\\4x=5*4\\x = 5[/tex]
g)
x : 2⁵ = 2²
x = 2⁵ · 2²
x = 2⁷
x = 128
h)
x + 2¹⁰ = 2¹⁰
x = 0
