Question

Determinați termenul necunoscut x știind că​

Answer 1

Răspuns:

• (A) x = 26
• (B) x = 1
• (C) x = 12
• (D) x = 2
• (E) x = 59
• (F) x = 1275

Explicație pas cu pas:

Salutare!

(A)

$\bf 3^{4}\cdot 3^{5}\cdot 3^{17} =3^{x}$

$\bf 3^{4+5+17} =3^{x}$

$\bf 3^{26} =3^{x}\implies \boxed{\bf x = 26}$

(B)

$\bf (5^{12}:5^{10}-4^{18}: 4^{16}):3^{2} = x$

$\bf (5^{12-10}-4^{18-16}):3^{2} = x$

$\bf (5^{2}-4^{2}):3^{2} = x$

$\bf (25-16):3^{2} = x$

$\bf 9:3^{2} = x$

$\bf 3^{2}:3^{2} = x$

$\bf 3^{2-2} = x$

$\bf 3^{0} = x$

$\boxed{\bf x = 1}$

(C)

$\bf [2^{5}\cdot(2\cdot3)^{7}]:3^{7} = 2^{x}$

$\bf (2^{5}\cdot 2^{7}\cdot3^{7}):3^{7} = 2^{x}$

$\bf (2^{5+7}\cdot3^{7}):3^{7} = 2^{x}$

$\bf 2^{12}\cdot3^{7-7} = 2^{x}$

$\bf 2^{12}\cdot3^{0} = 2^{x}$

$\bf 2^{12}\cdot 1 = 2^{x}$

$\bf 2^{12}= 2^{x}\implies \boxed{\bf x=12}$

(D)

$\bf (2^{3}\cdot3^{5})^{2}:(2^{4}\cdot3^{6}):3^{2}= 6^{x}$

$\bf (2^{3\cdot2}\cdot3^{5\cdot2}):(2^{4}\cdot3^{6}):3^{2}= 6^{x}$

$\bf (2^{6}\cdot3^{10}):(2^{4}\cdot3^{6}):3^{2}= 6^{x}$

$\bf 2^{6-4}\cdot3^{10-6}:3^{2}= 6^{x}$

$\bf 2^{2}\cdot3^{4}:3^{2}= 6^{x}$

$\bf 2^{2}\cdot3^{4-2}= 6^{x}$

$\bf 2^{2}\cdot3^{2}= 6^{x}$

$\bf (2\cdot3)^{2}= 6^{x}$

$\bf 6^{2}= 6^{x}\implies \boxed{\bf x= 2}$

(E)

$\bf (4\cdot 8)^{15}:4^{5}:2^{6}= 2^{x}$

$\bf (2^{2}\cdot 2^{3})^{15}:(2^{2})^{5}:2^{6}= 2^{x}$

$\bf (2^{2+3})^{15}:2^{2\cdot5}:2^{6}= 2^{x}$

$\bf (2^{5})^{15}:2^{10}:2^{6}= 2^{x}$

$\bf 2^{5\cdot 15}:2^{10}:2^{6}= 2^{x}$

$\bf 2^{75}:2^{10}:2^{6}= 2^{x}$

$\bf 2^{75-10-6}= 2^{x}$

$\bf 2^{59}= 2^{x}\implies \boxed{\bf x = 59}$

(F)

$\bf 2^{1}\cdot2^{2}\cdot 2^{3}\cdot2^{4}\cdot.........\cdot2^{50}=2^{x}$

$\bf 2^{1+2+3+4+.....+50} = 2^{x}$

$\bf 2^{50\cdot51:2} = 2^{x}$

$\bf 2^{1275} = 2^{x} \implies \boxed{\bf x = 1275}$

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