Question

Determinati termenul necunoscut c,stiind ca:
a)(7^x)^9=7^81
b)(8^5)^40=2^30•x
c)10^13=50^13:x^13
d)(20:x)^30=4^30​

Answer 1

Răspuns:

A) x=9…................

Answer 2

Explicație pas cu pas:

a)

$(7 {}^{x} ) {}^{9} = 7 {}^{81} \\ 7 {}^{9 \times x} = 7 {}^{81} \\ 9 \times x = 81 \\ x = 9$

b)

$(8 {}^{5} ) {}^{40} = 2 {}^{30 \times x } \\ 2 {}^{600 } = 2 {}^{30 \times x} \\ 600 = 30 \times x \\ x = 20$c)

$10 {}^{13} = 50 {}^{13} \div x {}^{13} \\ 10 {}^{13} = 5 {}^{13} \times 10 {}^{13} \div x {}^{13} \\ x {}^{13} = 5 {}^{13} \\ x = 5$

D)

$(20 \div x) {}^{30} = 4 {}^{30} \\ 20 {}^{30} \div x {}^{30} = 4 {}^{30} \\ 5 {}^{30} \times 4 {}^{30} \div x {}^{30} = 4 {}^{30} \\ 5 {}^{30} \div x{}^{30} = 1 \\ x {}^{30} = 5 {}^{30} \\ x = 5$