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5. Determinați numerele naturale x pentru care: a) [(2/5)²]^x•(2/5)³=(4/10)⁷
b)[(5/2)^x•]³(25/10)⁴=(5/2)¹⁰

va rooog frumos ajutați mă . că nu știu . ​


Răspuns :

Răspuns:

a)

[(2/5)²]^x•(2/5)³=(4/10)⁷

(2/5)²ˣ x (2/5)³ = (2/5)⁷

(2/5)²ˣ⁺³ = (2/5)⁷

2x + 3 = 7

2x = 7 - 3

2x = 4

x = 4/2

x = 2                            

b)

[(5/2)^x•]³(25/10)⁴=(5/2)¹⁰

(5/2)³ˣ x (5/2)⁴ = (5/2)¹⁰

(5/2)³ˣ⁺⁴ = (5/2)¹⁰

3x + 4 = 10

3x = 10 - 4

3x = 6

x = 6/3

x = 2

Vezi imaginea HAWKEYED

[tex]\it a)\ \ \ \bigg[\bigg(\dfrac{2}{5}\bigg)^2\bigg]^x\cdot\bigg(\dfrac{2}{5}\bigg)^3=\bigg(\dfrac{\ \ 4^{(2}}{10}\bigg)^7 \Rightarrow \bigg(\dfrac{2}{5}\bigg)^{2x}\cdot\bigg(\dfrac{2}{5}\bigg)^3=\bigg(\dfrac{2}{5}\bigg)^{7} \Rightarrow\\ \\ \\ \Rightarrow \bigg(\dfrac{2}{5}\bigg)^{2x+3}=\bigg(\dfrac{2}{5}\bigg)^7 \Rightarrow 2x+3=7\bigg|_{-3} \Rightarrow 2x=4\bigg|_{:2} \Rightarrow x=2[/tex]

[tex]\it b)\ \ \bigg[\bigg(\dfrac{5}{2}\bigg)^x\bigg]^3\cdot\bigg(\dfrac{\ \ 25^{(5}}{10}\bigg)^4=\bigg(\dfrac{5}{2}\bigg)^{10} \Rightarrow \bigg(\dfrac{5}{2}\bigg)^{3x} \cdot\bigg(\dfrac{5}{2}\bigg)^{4} =\bigg(\dfrac{5}{2}\bigg)^{10} \Rightarrow\\ \\ \\ \Rightarrow \bigg(\dfrac{5}{2}\bigg)^{3x+4} =\bigg(\dfrac{5}{2}\bigg)^{10} \Rightarrow 3x+4=10\bigg|_{-4} \Rightarrow 3x=6 \Rightarrow x=2[/tex]