Solve the Inequality for x log base 7 of x>=2

$\log_{7} (x) \geq 2$

Convert the inequality to an equality.

$\log_{7} (x) = 2$

Solve the equation.

Rewrite $\log_{7} (x) = 2$ 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 $b^{y} = x$ .

$7^{2} = x$

Solve for $x$ .

Rewrite the equation as $x = 7^{2}$ .

$x = 7^{2}$

Raise $7$ to the power of $2$ .

$x = 49$

Find the domain of $\log_{7} (x) - 2$ .

Set the argument in $\log_{7} (x)$ greater than $0$ to find where the expression is defined.

$x > 0$

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

$(0, \infty)$

The solution consists of all of the true intervals.

$x \geq 49$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 49$

Interval Notation:

$[49, \infty)$

Solve the Inequality for x log base 7 of x>=2

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