Answer:
[tex]x=11[/tex]
Step-by-step explanation:
Given the equation
[tex]\log_{15}(2x-2)=\log_{15}(x+9)[/tex]
Note that
[tex]2x-2>0\\ \\2x>2\\ \\x>1[/tex]
and
[tex]x+9>0\\ \\x>-9[/tex]
Combined, [tex]x>1[/tex]
Solve the equation:
[tex]2x-2= x+9\\ \\2x-x=9+2\\ \\x=11[/tex]
Since [tex]11>1,[/tex] this is the solution to the equation.
