Question

Solve the logarthmic equation.

2 log3(x + 4) - log39 = 2

Answer 1

does it help to know that \(\log_3(9)=2\) ?

Answer 2

that is because \(3^2=9\) so you have
\[2\log_3(x+4)-2=2\] or
\[2\log_3(x+4)=4\] or \[\log_3(x+4)=2\]

Answer 3

that means \(3^2=x+4\) and that is easy to solve

Answer 4

\[\log_{3} \left( x+4 \right)^2-\log_{3} 9=2\]
\[\log_{3} \frac{ \left( x+4 \right)^2 }{ 9 }=2\]
\[\log_{3} \left( \frac{ x+4 }{3 } \right)^2=2,2\log_{3} \frac{ x+4 }{ 3 }=2\]
\[\log_{3} \frac{ x+4 }{3 }=\frac{ 2 }{ 2 }=1,\frac{ x+4 }{3 }=3^1=3,x+4=9,x=?\]