Question

Решите уравнения log2 (8+7x)= log2 (8+3x)+1

Answer 1

log₂(8+7x)=log₂(8+3x)+1
ОДЗ:  
$left { {{8+7x textgreater 0} atop {8+3x textgreater 0}} right. , left { {{x textgreater - frac{8}{7} } atop {x textgreater - frac{8}{3} }} right. = textgreater x textgreater - frac{8}{7}$
1=log₂2¹=log₂2

log₂(8+7x)=log₂(8+3x)+log₂2
log₂(8+7x)=log₂((8+3x)*2)
8+7x=16+6x
x=8