Algebra Examples

$\log_{3} (x) > 4$

Step 1

Convert the inequality to an equality.

$\log_{3} (x) = 4$

Step 2

Solve the equation.

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Step 2.1

Rewrite $\log_{3} (x) = 4$ 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 $b^{y} = x$ .

$3^{4} = x$

Step 2.2

Solve for $x$ .

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Step 2.2.1

Rewrite the equation as $x = 3^{4}$ .

$x = 3^{4}$

Step 2.2.2

Raise $3$ to the power of $4$ .

$x = 81$

Step 3

Find the domain of $\log_{3} (x) - 4$ .

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Step 3.1

Set the argument in $\log_{3} (x)$ greater than $0$ to find where the expression is defined.

$x > 0$

Step 3.2

The domain is all values of $x$ that make the expression defined.

$(0, \infty)$

Step 4

The solution consists of all of the true intervals.

$x > 81$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 81$

Interval Notation:

$(81, \infty)$

Step 6