Question

$7 \times {5}^{x} - {5}^{x - 2} = 175$
Помогите решить, пожалуйста

Answer 1

$7\cdot 5^{x}-5^{x-2}=175\\\\7\cdot 5^{x}-5^{x}\cdot 5^{-2}=175\\\\7\cdot 5^{x}-\frac{1}{25}\cdot 5^{x}=175\\\\(7-\frac{1}{25})\cdot 5^{x}=175\\\\\frac{174}{25}\cdot5^{x}=175\\\\5^{x}=\frac{175\cdot 25}{174}\\\\5^{x}=\frac{4375}{174}\\\\x=log_5\, \frac{4375}{174}\\\\x=log_5\, 4375-log_5174=log_5(5^4\cdot 7)-log_5174\\\\x=4+log_57-log_5174$