Answer:
solution is x=3
Step-by-step explanation:
[tex]logx-log3=log(x-2)[/tex]
apply log property
log a- log b= log a/b
[tex]logx-log3=log(x-2)\\log (\frac{x}{3} )=log(x-2)[/tex]
we have log on both sides
so we remove the log and make the arguments equal
[tex]\frac{x}{3} = x-2[/tex]
solve for x, multiply whole equation by 3
[tex]x=3(x-2)\\x=3x-6\\x-3x=-6\\-2x=-6\\x=3[/tex]
now plug in 3 for x and check
[tex]logx-log3=log(x-2)\\log3-log3=log(3-2)\\0=0[/tex]
solution is x=3
