Trigonometry Examples

f (x) = \log_{0.3} (x)

$f (x) = \log_{0.3} (x)$

Step 1

Find the asymptotes.

Tap for more steps...

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

$x = 1$ .

Tap for more steps...

Step 2.1

Replace the variable

x

$x$ with

1

$1$ in the expression.

f (1) = \log_{0.3} (1)

$f (1) = \log_{0.3} (1)$

Step 2.2

Simplify the result.

Tap for more steps...

Step 2.2.1

Logarithm base

0.3

$0.3$ 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 = 2

$x = 2$ .

Tap for more steps...

Step 3.1

Replace the variable

x

$x$ with

2

$2$ in the expression.

f (2) = \log_{0.3} (2)

$f (2) = \log_{0.3} (2)$

Step 3.2

The final answer is

\log_{0.3} (2)

$\log_{0.3} (2)$ .

\log_{0.3} (2)

$\log_{0.3} (2)$

\log_{0.3} (2)

$\log_{0.3} (2)$

Step 4

Find the point at

x = 3

$x = 3$ .

Tap for more steps...

Step 4.1

Replace the variable

x

$x$ with

3

$3$ in the expression.

f (3) = \log_{0.3} (3)

$f (3) = \log_{0.3} (3)$

Step 4.2

The final answer is

\log_{0.3} (3)

$\log_{0.3} (3)$ .

\log_{0.3} (3)

$\log_{0.3} (3)$

\log_{0.3} (3)

$\log_{0.3} (3)$

Step 5

The log function can be graphed using the vertical asymptote at

x = 0

$x = 0$ and the points

(1, 0), (2, - 0.57571664), (3, - 0.91248928)

$(1, 0), (2, - 0.57571664), (3, - 0.91248928)$ .

Vertical Asymptote:

x = 0

$x = 0$

\begin{array}{c} x & y \\ 1 & 0 \\ 2 & - 0.576 \\ 3 & - 0.912 \end{array}

$\begin{array}{c} x & y \\ 1 & 0 \\ 2 & - 0.576 \\ 3 & - 0.912 \end{array}$

Step 6

f (x) = \log_{0.3} (x)

$f (x) = \log_{0.3} (x)$

(

)

[

]

√



≥















≤



































