Question

Решить уравнеие 2 в степени x+2 * 5 в степени х = 400

Answer 1

$2 {}^{x + 2} times 5 {}^{x} = 400 \ 2 {}^{x} times 2 {}^{2} times 5 {}^{x} = 40 0\2 {}^{x} times 4 times 5 {}^{x} = 400 \ (2 times 5) {}^{x} times 4 = 400 \ 10 {}^{x} times 4 = 400 \ 10 {}^{x} = 100 \ 10 {}^{x} = 10 {}^{2} \ x = 2$

Answer 2

$2^{x+2} *5^{x}$ = 400

$2^{x} * 2^{2} * 5^{x} = 400$

$2^{x} * 4 * 5^{x} = 400$

$(2*5)^{x} * 4 = 400$

$10^{x} *4 = 400$

$10^{x} = 100$

$10^{x} = 10^{2}$

x = 2