Log2(x+3) + log2(x+2)= log2 6

Question

Log2(x+3) + log2(x+2)= log2 6

Answer 1

log2(x+3)+log2(x+2)=log2(6)

x+3>0 =>x>-3

x+2>0 => x>-2

log2[(x+3)(x+2)]=log2(6)

(x+3)(x+2)=6

x^2+3x+2x+6=6

x^2+5x=0

x(x+5)=0

a) x=0

б) x+5=0 => x=-5 - не удовлетворяет ОДЗ

 

ответ x=0