Rozwiąż równanie logarytmiczne. log(x-2)+log3=3 logx-2logx

[latex]log(x-2) + log3 = 3logx - 2logx\\x extgreater 0\i\x-2 extgreater 0\x extgreater 2\\log3(x-2) = logx^{3} - logx^{2}\\log(3x-6) = logfrac{x^{3}}{x^{2}}\\log(3x-6) = logx\\3x - 6 = x\\3x-x = 6\\2x = 6 /:2\\x = 3[/latex]