Question

решите уравнение
а)log 5 (7-x)=log 5(3-x)+1
б)log x 32=5​

Answer 1

а)ОДЗ 7-x>0 x <7

3-x>0 x <3

$log_{5}(7 - x )= log_{5}(3 - x) + log_{5}5 \\ log_{5}(7 - x) = log_{5}5(3 - x) \\ 7 - x = 15 - 5x \\ 4x = 8 \\ x = 2$

б)

${x}^{5} = 32 \\ {x}^{5} = {2}^{5} \\ x = 2$