Question

5 la puterea x+2-2*5 la putereax+1-12*5la putereax=375​

Answer 1

Răspuns:

3

Explicație pas cu pas:

5^(x+2)-2*5^(x+1)-12*5^x=375

5^x*5^2-2*5^x*5-12*5^x=375

25*5^x-10*5^x-12*5^x=375

5^x(25-10-12)=375

3*5^x=375

5^x=125

5^x=5^3

(Cum functia exponentiala este injectiva, avem)

x=3

Answer 2

${5}^{x + 2} - 2 \times 5 {}^{x + 1} - 12 \times 5 {}^{x} = 37$

$( {5}^{2} - 2 \times 5 - 12) \times 5 {}^{x} = 375$

$(25 - 10 - 12) \times 5 {}^{x} = 375$

$3 \times 5 {}^{x} = 375$

$5 {}^{x} = 125$

$5 {}^{x} = {5}^{3}$

$x = 3$