Question

. Determinați numărul natural x care verifică egalitatea:
a) (4^x)²=2⁸

b) (10^x)⁵•100=(2⁴•5⁴)⁸

VA ROG REPEDE DAU 100 DEPUNCTE SI COROANA​

Answer 1

Răspuns:

$\red{\bf a) ~~x = 2}$

$\purple{\bf b)~~x=6}$

Explicație pas cu pas:

$\bf a) ~ \big(4^x\big)^2=2^8$

$\bf \big[\big(2^{2} \big)^x\big]^2=2^8$

$\bf \big(2^{2\cdot x} \big)^2=2^8$

$\bf 2^{2 x\cdot 2}=2^8$

$\bf 2^{4 x}=2^8\Rightarrow 4x = 8\Rightarrow x = 8 : 4 \Rightarrow \red{\underline{x = 2}}$

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$\bf b) ~ \big(10^x\big)^5\cdot 100=\big(2^4\cdot 5^{4}\big)^8$

$\bf 10^{x \cdot 5}\cdot 10^{2} =\big[\big(2\cdot 5\big)^{4}\big]^8$

$\bf 10^{5x}\cdot 10^{2} =\big(10^{4}\big)^8$

$\bf 10^{5x+2} =10^{4\cdot 8}$

$\bf 10^{5x+2} =10^{32}\Rightarrow 5x+2=32\Rightarrow$

$\bf 5x=32-2\Rightarrow 5x = 30\Rightarrow x = 30 : 5\Rightarrow \purple{\underline{x=6}}$

În imagine ai câteva formule pentru puteri.

==pav38==

Baftă multă !

Answer 2

$\it a)\ (4^x)^2=2^8 \Rightarrow 4^{2x}= 2^{2\cdot4} \Rightarrow 4^{2x}=(2^2)^4 \Rightarrow 4^{2x}=4^4 \Rightarrow 2x=4 \Rightarrow x=2\\ \\ \\b)\ (10^x)^5\cdot100=(2^4\cdot5^4)^8 \Rightarrow 10^{5x}\cdot10^2=(2\cdot5)^{4\cdot8} \Rightarrow 10^{5x+2}=10^{32}\\ \\ \\ 5x+2=32\bigg|_{-2} \Rightarrow 5x=30 \Rightarrow x=6$