Question

1. ile zer mają podane liczby w zapisie dziesiętnym?
a=5*10^8
b=4,97*10^17
c=8,5936*10^29
d=7,368*10^103

2.Znajdź x:
a)2^x=1/8
b)2^x=0,25
c)2^x=0,0625
d)0,5^x=0,25
e)0,5^x=1/8
f)0,5^x=32
g)0,1^x=1000
h)1,5^x=2/3
i)1,25^x=0,512

Answer 1

1. ile zer mają podane liczby w zapisie dziesiętnym?
a=5*10^8    ( 8 zer na końcu liczby)

b=4,97*10^17 ( 15 zer na końcu liczby)

b = 497*10²*10¹⁷ = 497*10¹⁵

c=8,5936*10^29

c = 85936*10⁻⁴*10²⁹

c =85936*10²⁵ ( 25 zer na kńcu liczby

 
d=7,368*10^103

d = 7368*10⁻³*10¹⁰³

d = 7368*10¹⁰⁰  ( 100 zer na końcu liczby)

2.Znajdź x:
a)2^x=1/8

  2^x = (½)³

  2^x = 2⁻³

    x = -3

 
b)2^x=0,25

   2^x = ¼

   2^x = (½)²

   2^x =  2⁻²

      x = -2

c)2^x=0,0625

   2^x = 625/10000

    2^x = 1/16

    2^x = (½)⁴

    2^x =  2⁻⁴

       x = -4

d)0,5^x=0,25

   (½)^x = ¼

    (½)^x = (½)²

         x = 2

e)0,5^x=1/8

  (½)^x = (½)³

        x =  3

f)0,5^x=32

  (½)^x = 2⁵

  (½)^x = (½)⁻⁵

     x = -5

g)0,1^x=1000

  (1/10)^x = 10³

  (1/10)^x = (1/10)⁻³

   x = -3

h)1,5^x=2/3

  (3/2)^x = (2/3)¹

  (3/2)^x = (3/2)⁻¹

     x = -1

 

 

i)1,25^x=0,512

  (5/4)^x =  (512/1000)

  (5/4)^x = (64/125)

  (5/4)^x = (4³/ 5³)

  (5/4)^x = (4/5)³

   (5/4)^x = (5/4)⁻³

        x = -3