Question

Find the domain of the function.f(x) = log5 (2x - 2)

Answer 1

`\begin{gathered} \text{Given} \\ f(x)=\log _5(2x-2) \end{gathered}`

Recall that the parameter for the logarithmic function cannot be negative since it is undefined.

Therefore, we have to solve for 2x - 2, such that the result will not be negative.

`\begin{gathered} 2x-2>0 \\ \text{Add }2\text{ to both sides} \\ 2x-2+2>0+2 \\ 2x\cancel{-2+2}>2 \\ 2x>2 \\ \\ \text{Divide both sides by }2 \\ (2x)/(2)>(2)/(2) \\ x>1 \end{gathered}`

Since x > 1, we can conclude that the domain of the function f(x) is

`\text{Domain: }(1,\infty)`