Question

Решить уравнение:log2(x-4)+log2(x-19)=log2 250
Вычислите:3^2+log3 10

Answer 1

$log_2(x-4)+log_2(x-19)=log_2250 \ log_2(x-4)(x-19)=log_2250 \ (x-4)(x-19)=250 \ x^2-4x-19x+76=250 \ x^2-23x-174=0 \ D=1225 \ x_1=-6 \ x_2=29 \ x-4 textgreater 0 \ x textgreater 4 \ x-19 textgreater 0 \ x textgreater 19$

x = -6 не удовлетворяет ОДЗ

Ответ. х = 29

Answer 2

1)
log₂(x - 4) + log₂(x - 19) = log₂250
$left { {{log_2((x-4)(x-19))=log_2250} atop {x-4 textgreater 0}} right. \ left { {{(x-4)(x-19)=250} atop {x textgreater 4}} right. \ left { {{x^2-23x+76=250} atop {x textgreater 4}} right. \ left { {{x^2-23x-174=0} atop {x textgreater 4}} right. \ left { {{x_1=-6; x_2=29} atop {x textgreater 4}} right. \ x=29$
2)
$3^{2+log_310}=9*3^{log_310}=9*10=90$