Question

Determine the domain of the following log function algebraically. f(x) = log5 (2x-1)

Answer 1

ANSWER:

$(\frac{1}{2},\infty)$

EXPLANATION:

Remember that any logarithm is capable of recieveng numbers that are greater than zero. This way, we'll have the restriction:

$2x-1>0$

Solving for x,

$\begin{gathered} 2x-1>0 \\ \rightarrow2x>1 \\ \\ \Rightarrow x>\frac{1}{2} \end{gathered}$

This way, the domain is:

$(\frac{1}{2},\infty)$