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