Question

Solve allgebraically for x: log base 27 (2x-1)=4/3

Answer 1

`log_(27)(2x-1)=(4)/(3);\ \ \ \ D:2x-1 > 0\to x > (1)/(2)\\\\log_(27)(2x-1)=log_(27)27^(4)/(3)\iff 2x-1=27^(4)/(3)\\\\2x-1=\left(\sqrt[3]{27}\right)^4\\\\2x-1=3^4\\\\2x-1=81\ \ \ /+1\\\\2x=82\ \ \ \ /:2\\\\x=41\in D`