Question

Решите уравнение логорифмическое

Answer 1

х+1≠0
х≠ -1
$\frac{x+4}{15} \ \textgreater \ 0 \\ x+4\ \textgreater \ 0 \\ x\ \textgreater \ -4 \\ \frac{5}{x+1} \ \textgreater \ 0 \\ x+1\ \textgreater \ 0 \\ x\ \textgreater \ -1$ 
x∈(-1; +∞) 
$log _{7} ( \frac{x+4}{15} * \frac{5}{x+1}) = 1 \\ log_{7} ( \frac{x+4}{3(x+1)}) =1 \\ \frac{x+4}{3(x+1)} = 7^{1} \\ \frac{x+4}{3(x+1)} =7 \\ x+4 =3*7(x+1) \\ x+4 = 21(x+1) \\ x+4 =21x +21 \\ x-21x = 21-4 \\ -20x = 17 \\ x = - \frac{17}{20}$
x = -0.85

Answer 2

$log_{7}( \frac{x + 4}{15} \times \frac{5}{x + 1} ) = log_{7}(7) \\ \frac{x + 4}{15} \times \frac{5}{x + 1} = 7 \\ \frac{5x + 20}{15x + 15} = 7 \\ 5x + 20 = 7(15x + 15) \\ 5x + 20 = 105x + 105 \\ - 100x = 85 \\ x = - 0.85$