Question

Решите уравнение.

$5^{x+2} +11*5^{x} = 180$

Answer 1

${5}^{x + 2} + 11 \times {5}^{x} = 180 \\ {5}^{x} \times {5}^{2} + 11 \times {5}^{x} = 180 \\ {5}^{x}(25 + 11) = 180 \\ {5}^{x} \times 36 = 180 \\ {5}^{x} = 180 \div 36 \\ {5}^{x} = {5}^{1} \\ x = 1$

Answer 2

5^(х + 2) + 11 • 5^х = 180
5^х • 25 + 11 • 5^х = 180
5^х • (25 + 11) = 180
5^х • 36 = 180
5^х = 5
5^х = 5^1, так как 5 > 1, то у = 5^ф возрастает.
х = 1
Ответ: 1.