Graph y=- log base 5 of -x

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

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$- x = 0$

Divide each term in $- x = 0$ by $- 1$ and simplify.

Divide each term in $- x = 0$ by $- 1$ .

$\frac{- x}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{0}{- 1}$

Divide $x$ by $1$ .

$x = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

$x = 0$

The vertical asymptote occurs at $x = 0$ .

Vertical Asymptote: $x = 0$

Step 2

Find the point at $x = - 1$ .

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = - \log_{5} (- (- 1))$

Simplify the result.

Multiply $- 1$ by $- 1$ .

$f (- 1) = - \log_{5} (1)$

Logarithm base $5$ of $1$ is $0$ .

$f (- 1) = - 0$

Multiply $- 1$ by $0$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$= 0$

Step 3

Find the point at $x = - 2$ .

Replace the variable $x$ with $- 2$ in the expression.

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

Simplify the result.

Multiply $- 1$ by $- 2$ .

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

The final answer is $- \log_{5} (2)$ .

$- \log_{5} (2)$

Convert $- \log_{5} (2)$ to decimal.

$= - 0.43067655$

Step 4

Find the point at $x = - 3$ .

Replace the variable $x$ with $- 3$ in the expression.

$f (- 3) = - \log_{5} (- (- 3))$

Simplify the result.

Multiply $- 1$ by $- 3$ .

$f (- 3) = - \log_{5} (3)$

The final answer is $- \log_{5} (3)$ .

$- \log_{5} (3)$

Convert $- \log_{5} (3)$ to decimal.

$= - 0.68260619$

Step 5

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(- 1, 0), (- 2, - 0.43067655), (- 3, - 0.68260619)$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ - 3 & - 0.683 \\ - 2 & - 0.431 \\ - 1 & 0 \end{array}$

Step 6

Graph y=- log base 5 of -x

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