Solve for x log base b of 25=2

$\log_{b} (25) = 2$

Rewrite $\log_{b} (25) = 2$ 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 $b^{y} = x$ .

$b^{2} = 25$

Solve for $b$

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Take the $(+2)th$ root of both sides of the $equation$ to eliminate the exponent on the left side.

$b = \pm \sqrt{25}$

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

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Simplify the right side of the equation.

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Rewrite $25$ as $5^{2}$ .

$b = \pm \sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$b = \pm 5$

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 first solution.

$b = 5$

Next, use the negative value of the $\pm$ to find the second solution.

$b = - 5$

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

$b = 5, - 5$

Exclude the solutions that do not make $\log_{b} (25) = 2$ true.

$b = 5$

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