Questions: What is the x-intercept of the logarithmic function below? F(x)=log3 x A. (1,0) B. (-3,0) C. (3,0) D. (-1,0)

Solution Steps

The \(x\)-intercept of a function occurs where the graph of the function crosses the \(x\)-axis. At this point, the \(y\)-value is 0.

To find the \(x\)-intercept, set \(F(x) = 0\): \[ \log _{3} x = 0 \]

Rewrite the logarithmic equation in its exponential form: \[ 3^0 = x \] Since \(3^0 = 1\), we have: \[ x = 1 \]

The \(x\)-intercept is the point where \(x = 1\) and \(y = 0\), which corresponds to the point \((1, 0)\).

Final Answer