Question

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Answer 1

Răspuns:

a)

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

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

$\bf 3^{26} =3^{x}\implies \green{\underline{~ x = 26~}}$

b)

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

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

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

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

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

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

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

$\bf 3^{0} = x$

$\blue{\underline{\bf~ x = 1~}}$

c)

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

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

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

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

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

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

$\bf 2^{12}= 2^{x}\implies \purple{\underline{\bf~ x=12~}}$

d)

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

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

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

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

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

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

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

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

$\bf 6^{2}= 6^{x}\implies \pink{\underline{\bf ~x= 2~}}$

e)

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

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

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

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

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

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

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

$\bf 2^{59}= 2^{x}\implies \red{\underline{\bf ~x = 59~}}$

f)

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

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

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

$\bf 2^{1275} = 2^{x} \implies \purple{\underline{\bf~x = 1275~}}$