Find the x and y Intercepts f(x) = log base 1/2 of x+3

$f (x) = \log_{\frac{1}{2}} (x) + 3$

Step 1

Find the x-intercepts.

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

$0 = \log_{\frac{1}{2}} (x) + 3$

Solve the equation.

Rewrite the equation as $\log_{\frac{1}{2}} (x) + 3 = 0$ .

$\log_{\frac{1}{2}} (x) + 3 = 0$

Subtract $3$ from both sides of the equation.

$\log_{\frac{1}{2}} (x) = - 3$

Rewrite $\log_{\frac{1}{2}} (x) = - 3$ 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 $b^{y} = x$ .

${(\frac{1}{2})}^{- 3} = x$

Solve for $x$ .

Rewrite the equation as $x = {(\frac{1}{2})}^{- 3}$ .

$x = {(\frac{1}{2})}^{- 3}$

Simplify ${(\frac{1}{2})}^{- 3}$ .

Change the sign of the exponent by rewriting the base as its reciprocal.

$x = 2^{3}$

Raise $2$ to the power of $3$ .

$x = 8$

x-intercept(s) in point form.

x-intercept(s): $(8, 0)$

Step 2

Find the y-intercepts.

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

$y = \log_{\frac{1}{2}} (0) + 3$

Solve the equation.

The logarithm of zero is undefined.

$y = Undefined$

Remove parentheses.

$y = \log_{\frac{1}{2}} (0) + 3$

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): $(8, 0)$

y-intercept(s): $None$

Step 4

Find the x and y Intercepts f(x) = log base 1/2 of x+3

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