Question

log_9 (2x+7)-log_9 (x-1)=log_9 (x-7) ayúdenme por favor

Answer 1

Respuesta:

$log_9 (2x+7)-log_9 (x-1)=log_9 (x-7) \\ log_{9}( \frac{2x + 7}{x - 1} ) = log_{9}(x - 7) \\ {9}^{ log_{9}( \frac{2x + 7}{x - 1} ) } = {9}^{ log_{9}(x - 7) } \\ \frac{2x + 7}{x - 1} = x - 7 \\ 2x + 7 = (x - 7)(x - 1) \\ 2x + 7 = {x}^{2} - x - 7x + 7 \\ 2x + 7 = {x}^{2} - 8x + 7 \\ {x}^{2} - 8x + 7 - 2x - 7 = 0 \\ {x}^{2} - 10x = 0 \\ x(x - 10) = 0 \\ x - 10 = \frac{0}{x} \\ x - 10 = 0 \\ x = 10$