Recall the following property of logarithms:
[tex]\log _a(b)=c\Leftrightarrow b=a^c[/tex]Then:
[tex]\begin{gathered} \log _2(5x-4)=4 \\ \Leftrightarrow \\ 5x-4=2^4 \end{gathered}[/tex]Solve for x in the new equation:
[tex]\begin{gathered} 5x-4=2^4 \\ \Rightarrow5x-4=16 \\ \Rightarrow5x=16+4 \\ \Rightarrow5x=20 \\ \Rightarrow x=\frac{20}{5} \\ \Rightarrow x=4 \end{gathered}[/tex]Replace x=4 into the original expression to confirm the result:
[tex]\begin{gathered} \log _2(5x-4)=\log _2(5(4)-4) \\ =\log _2(20-4) \\ =\log _2(16) \\ =4 \end{gathered}[/tex]Therefore, the answer is: x=4
