# How do you find the domain of f(x)=log_8(x+1)?

Jul 24, 2018

$\text{ }$
$\textcolor{red}{\left[x > \left(- 1\right)\right)}$ is the required domain of $\textcolor{red}{f \left(x\right)}$

Using interval notation:

color(red)((-1,oo)

#### Explanation:

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Domain of a function can be defined a s a set of input values for which the function is real and defined .

We are given the function:

color(blue)(y=f(x)=log_8(x+1)

Use positive values only for this problem:

color(red)(x+1>0

Subtract color(blue)(1 from both sides

$\Rightarrow \left[\left(x + 1\right) - 1\right] > 0 - 1$

$\Rightarrow \left[\left(x + 1\right) - 1\right] > 0 - 1$

$\Rightarrow x + 1 - 1 > 0 - 1$

$\Rightarrow x + \cancel{1} - \cancel{1} > 0 - 1$

$\Rightarrow x > \left(- 1\right)$

Hence, our final solution is:

$\textcolor{red}{\left[x > \left(- 1\right)\right)}$ is the required domain of $\textcolor{red}{f \left(x\right)}$

Using interval notation:

color(red)((-1,oo)

Hope this helps.