Find the x and y Intercepts f(x)=-2+ log base 5 of -x

$f (x) = - 2 + \log_{5} (- x)$

Step 1

Find the x-intercepts.

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

$0 = - 2 + \log_{5} (- x)$

Solve the equation.

Rewrite the equation as $- 2 + \log_{5} (- x) = 0$ .

$- 2 + \log_{5} (- x) = 0$

Add $2$ to both sides of the equation.

$\log_{5} (- x) = 2$

Rewrite $\log_{5} (- x) = 2$ 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 $b^{y} = x$ .

$5^{2} = - x$

Solve for $x$ .

Rewrite the equation as $- x = 5^{2}$ .

$- x = 5^{2}$

Divide each term in $- x = 5^{2}$ by $- 1$ and simplify.

Divide each term in $- x = 5^{2}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{5^{2}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{5^{2}}{- 1}$

Divide $x$ by $1$ .

$x = \frac{5^{2}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{5^{2}}{- 1}$ .

$x = - 1 \cdot 5^{2}$

Rewrite $- 1 \cdot 5^{2}$ as $- 5^{2}$ .

$x = - 5^{2}$

Raise $5$ to the power of $2$ .

$x = - 1 \cdot 25$

Multiply $- 1$ by $25$ .

$x = - 25$

x-intercept(s) in point form.

x-intercept(s): $(- 25, 0)$

Step 2

Find the y-intercepts.

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

$y = - 2 + \log_{5} (- (0))$

Solve the equation.

Remove parentheses.

$y = - 2 + \log_{5} (- (0))$

Simplify the right side.

Multiply $- 1$ by $0$ .

$y = - 2 + \log_{5} (0)$

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): $(- 25, 0)$

y-intercept(s): $None$

Step 4

Find the x and y Intercepts f(x)=-2+ log base 5 of -x

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