Solve for x log base x of sixteen equals four

$\log_{x} (16) = 4$

Should be rewritten $\log_{x} (16) = 4$ 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 $b^{y} = x$ .

$x^{4} = 16$

Calculate $x$

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Take the $(+4)th$ root of both sides of the $equation$ to eliminate the exponent on the left side.

$x = \pm \sqrt[4]{16}$

The total solution is the sum of the solution's positive and negative components.

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Clarify the right side of the equation.

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Rewrite $16$ as $2^{4}$ .

$x = \pm \sqrt[4]{2^{4}}$

Withdraw terms from under the radical, assuming positive real numbers.

$x = \pm 2$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the Initially solution.

$x = 2$

Next, use the negative value of the $\pm$ To calculate the second answer.

$x = - 2$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2, - 2$

Exclude the solutions that do not make $\log_{x} (16) = 4$ true.

$x = 2$

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