Question

Znajdz liczby a, b i c
A) 2^12=4^a=8^b=64^c
B) 10^20=100^a=10000^b=100000^c

Fajnie by bylo jakby ktos mi to wytlumaczyl

Answer 1

Odpowiedź:

A.   [tex]2^{12} = 4^a = (2^2)^a = 2^{2a}[/tex]

2 a = 12

a = 6

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[tex]8^b = (2^3)^b = 2^{3 b} = 2^{12}[/tex]

3 b = 12

b = 4

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[tex]64^c = ( 2^6)^b = 2^{6c} = 2^{12}[/tex]

6 c = 12

c = 2

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Odp.  [tex]2^{12} = 4^{6} = 8^4 = 64^{2}[/tex]

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B.

[tex]10^{20} = 100^a = (10^2)^a = 10^{2a}[/tex]

2 a = 20

a = 10

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10 000[tex]^b =[/tex]  ( [tex]10^4)^b = 10^{4b}[/tex]

4 b = 20

b = 5

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100 000[tex]^c = ( 10^5)^c = 10^{5 c}[/tex]

5 c = 20

c = 4

Odp.   [tex]10^{20} = 100^{10} = 10 000^5 = 100 000^4[/tex]

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