Find the x and y Intercepts f(x) = log base 1/3 of x-4

$f (x) = \log_{\frac{1}{3}} (x - 4)$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \log_{\frac{1}{3}} (x - 4)$

Solve the equation.

Rewrite the equation as $\log_{\frac{1}{3}} (x - 4) = 0$ .

$\log_{\frac{1}{3}} (x - 4) = 0$

Rewrite $\log_{\frac{1}{3}} (x - 4) = 0$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

${(\frac{1}{3})}^{0} = x - 4$

Solve for $x$ .

Rewrite the equation as $x - 4 = {(\frac{1}{3})}^{0}$ .

$x - 4 = {(\frac{1}{3})}^{0}$

Simplify ${(\frac{1}{3})}^{0}$ .

Apply the product rule to $\frac{1}{3}$ .

$x - 4 = \frac{1^{0}}{3^{0}}$

Anything raised to $0$ is $1$ .

$x - 4 = \frac{1}{3^{0}}$

Anything raised to $0$ is $1$ .

$x - 4 = \frac{1}{1}$

Divide $1$ by $1$ .

$x - 4 = 1$

Move all terms not containing $x$ to the right side of the equation.

Add $4$ to both sides of the equation.

$x = 1 + 4$

Add $1$ and $4$ .

$x = 5$

x-intercept(s) in point form.

x-intercept(s): $(5, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \log_{\frac{1}{3}} ((0) - 4)$

Solve the equation.

The logarithm of a negative number is undefined.

$y = Undefined$

Remove parentheses.

$y = \log_{\frac{1}{3}} ((0) - 4)$

The equation cannot be solved because it is undefined.

$Undefined$

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(5, 0)$

y-intercept(s): $None$

Step 4

Find the x and y Intercepts f(x) = log base 1/3 of x-4

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