Question

Aflați numărul natural x care verifică fiecare relație:
a)(3^x)⁴×3³=3²⁷
b)(7⁵)^x=(7³)¹⁰
c)(10^x)⁴×10000=(10⁸)⁵
VĂ ROG REPEDE!
DAU COROANĂ!​

Answer 1

$(x^{n} )^{y} = x^{n*x} \\\\x^{n} * x^y =x^{n+y}$

a) (3^x)⁴×3³=3²⁷

 $3^{4*x+3} =3^{27} /:3^{3} \\3^{4x} = 3^{24} \\x= 24/4=6$

b)

$7^{5x} = 7^{3*10} \\7^{5x} = 7^{30}\\x=30/5=6$

c) $10^{4x} *10000= 10^{40} \\10^{4x} *10^{4} = 10^{40}\\10^{4x+4}= 10^{40} / : 10^{4} \\10^{4x} = 10^{36} \\x=36/4=9$