# Evaluate: f(x)=log_{10}(3x-21)

## Expression: $f\left( x \right)=\log_{ 10 }({ 3x-21 })$

Separate the function into parts to determine the domain of each part

$\begin{array} { l }\log_{ 10 }({ 3x-21 }),\\3x-21\end{array}$

The domain of a logarithmic function are all values of $x$ for which the argument is positive

$\begin{array} { l }x > 7,\\3x-21\end{array}$

The domain of a linear function is the set of all real numbers

$\begin{array} { l }x > 7,\\x \in ℝ\end{array}$

Find the intersection

\begin{align*}&x \in \langle7, +\infty\rangle \\&\begin{array} { l }x > 7\end{array}\end{align*}

Random Posts
Random Articles