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zadanie 16 tylko podpunkt c) i d)



Zadanie 16 Tylko Podpunkt C I D class=

Odpowiedź :

Basetla

16.

c)

[tex]4^{5}\cdot x = (2^{2})^{10}\\\\(2^{2})^{5} \cdot x = (2^{2})^{10}\\\\2^{2\cdot5}\cdot x = 2^{2\cdot10}\\\\2^{10}\cdot x = 2^{20} \ \ /:2^{10}\\\\x = 2^{20-10}\\\\x = 2^{10}\\\\\underline{x = 1024}[/tex]

d)

[tex]27^{3}+25^{3} =3^{9}+5^{4}\cdot x\\\\3^{9}+5^{4}\cdot x = 27^{3}+25^{3}\\\\5^{4}x = (3^{3})^{3} + (5^{2})^{3}-3^{9}\\\\5^{4}x = 3^{3\cdot 3}+5^{2\cdot3}-3^{9}\\\\5^{4}x = 3^{9}+5^{6}-3^{9}\\\\5^{4}x = 5^{6} \ \ /:5^{4}\\\\x = 5^{6-4}\\\\x = 5^{2}\\\\\underline{x = 25}[/tex]

Magda

Odpowiedź:

[tex]c)\\\\4^5\cdot x=(2^2)^{10}\\\\(2^2)^5x=2^{20}\\\\2^{10}x=2^{20}\ \ /:2^{10}\\\\x=2^{20}:2^{10}\\\\x=2^{20-10}\\\\x=2^{10}\\\\x=1024\\\\\\d)\\\\27^3+25^3=3^9+5^4x\\\\(3^3)^3+(5^2)^3=3^9+5^4x\\\\3^9+5^6=3^9+5^4x\\\\\not3^9+5^6-\not3^9=5^4x\\\\5^6=5^4x\\\\5^4x=5^6\ \ /:5^4\\\\x=5^6:5^4\\\\x=5^{6-4}\\\\x=5^2\\\\x=25[/tex]

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