Răspuns:
- (a) x = 26
- (c) x = 12
- (d) x = 2
Explicație pas cu pas:
Salutare!
(d)
[tex]\bf (2^{3}\cdot 3^{5})^{2}:(2^{4}\cdot 3^{6}):3^{2}=6^{x}[/tex]
[tex]\bf 2^{3\cdot2}\cdot 3^{5\cdot 2}:2^{4}\cdot 3^{6}:3^{2}=6^{x}[/tex]
[tex]\bf 2^{6}\cdot 3^{10}:2^{4}\cdot 3^{6}:3^{2}=6^{x}[/tex]
[tex]\bf 2^{6-4}\cdot 3^{10-6-2}=6^{x}[/tex]
[tex]\bf 2^{2}\cdot 3^{2}=6^{x}[/tex]
[tex]\bf (2\cdot 3)^{2}=6^{x}[/tex]
[tex]\bf 6^{2}=6^{x} \implies \boxed{\bf x = 2}[/tex]
(a)
[tex]\bf 3^{4}\cdot 3^{5}\cdot 3^{17}=3^{x}[/tex]
[tex]\bf 3^{4+5+17}=3^{x}[/tex]
[tex]\bf 3^{26}=3^{x}\implies \boxed{\bf x = 26}[/tex]
(c)
[tex]\bf [2^{5} \cdot (2\cdot3)^{7}]: 3^{7}=2^{x}[/tex]
[tex]\bf 2^{5} \cdot 2^{7}\cdot3^{7}: 3^{7}=2^{x}[/tex]
[tex]\bf 2^{5+7} \cdot3^{7-7}=2^{x}[/tex]
[tex]\bf 2^{12} \cdot3^{0}=2^{x}[/tex]
[tex]\bf 2^{12} \cdot 1=2^{x}[/tex]
[tex]\bf 2^{12} =2^{x}\implies\boxed{\bf x = 12}[/tex]
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