Algebra Examples

\log_{5} (x)

$\log_{5} (x)$

Step 1

Find the asymptotes.

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Step 1.1

Set the argument of the logarithm equal to zero.

x = 0

$x = 0$

Step 1.2

The vertical asymptote occurs at

x = 0

$x = 0$ .

Vertical Asymptote:

x = 0

$x = 0$

Vertical Asymptote:

x = 0

$x = 0$

Step 2

Find the point at

x = 1

$x = 1$ .

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Step 2.1

Replace the variable

x

$x$ with

1

$1$ in the expression.

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

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

Step 2.2

Simplify the result.

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Step 2.2.1

Logarithm base

5

$5$ of

1

$1$ is

0

$0$ .

f (1) = 0

$f (1) = 0$

Step 2.2.2

The final answer is

0

$0$ .

0

$0$

0

$0$

Step 2.3

Convert

0

$0$ to decimal.

y = 0

$y = 0$

y = 0

$y = 0$

Step 3

Find the point at

x = 5

$x = 5$ .

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Step 3.1

Replace the variable

x

$x$ with

5

$5$ in the expression.

f (5) = \log_{5} (5)

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

Step 3.2

Simplify the result.

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Step 3.2.1

Logarithm base

5

$5$ of

5

$5$ is

1

$1$ .

f (5) = 1

$f (5) = 1$

Step 3.2.2

The final answer is

1

$1$ .

1

$1$

1

$1$

Step 3.3

Convert

1

$1$ to decimal.

y = 1

$y = 1$

y = 1

$y = 1$

Step 4

Find the point at

x = 2

$x = 2$ .

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Step 4.1

Replace the variable

x

$x$ with

2

$2$ in the expression.

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

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

Step 4.2

The final answer is

\log_{5} (2)

$\log_{5} (2)$ .

\log_{5} (2)

$\log_{5} (2)$

Step 4.3

Convert

\log_{5} (2)

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

y = 0.43067655

$y = 0.43067655$

y = 0.43067655

$y = 0.43067655$

Step 5

The log function can be graphed using the vertical asymptote at

x = 0

$x = 0$ and the points

(1, 0), (5, 1), (2, 0.43067655)

$(1, 0), (5, 1), (2, 0.43067655)$ .

Vertical Asymptote:

x = 0

$x = 0$

\begin{array}{c} x & y \\ 1 & 0 \\ 2 & 0.431 \\ 5 & 1 \end{array}

$\begin{array}{c} x & y \\ 1 & 0 \\ 2 & 0.431 \\ 5 & 1 \end{array}$

Step 6