remember
[tex]log_a(b)=c[/tex] translates to [tex]a^c=b[/tex]
and
[tex]log_a(b^c)=clog_a(b)[/tex]
so
4096=16^3
[tex]log_{3x-2}(4096)=3[/tex]
[tex]log_{3x-2}(16^3)=3[/tex]
[tex]3log_{3x-2}(16)=3[/tex]
divide both sides by 3
[tex]log_{3x-2}(16)=1[/tex]
translate
[tex](3x-2)^1=16[/tex]
3x-2=16
add 2 to both sides
3x=18
divide both sides by 3
x=6
