Question

Log2(2x+15)=log2 3-1

Answer 1

log2(2x+15)=log2 3-1
=>log2(2x+15)=log2 3 - log2 2
=>log2(2x+15)=log2 3/2
=> 2x+15=3/2
=>4x+30=3
=>4x=-27
=>x=-27/4

Answer 2

ОДЗ: 2x + 15 > 0   ⇒  2x > - 15      ⇒  x > - 7,5
$log _{2}(2x+15)= log _{2}3-1\\\\log _{2}(2x+15)=log _{2}3-log _{2}2\\\\log _{2}(2x+15)=log _{2}1,5\\\\2x+15=1,5\\\\2x=-13,5\\\\x= -6,75$