Rewrite <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mn>25</mn><mo>)</mo></mrow><mo>=</mo><mn>2</mn></mstyle></math> in exponential form using the definition of a logarithm. If <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> are positive real numbers and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> <math><mstyle displaystyle="true"><mo>≠</mo></mstyle></math> <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> , then <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>y</mi></mstyle></math> is equivalent to <math><mstyle displaystyle="true"><msup><mrow><mi>b</mi></mrow><mrow><mi>y</mi></mrow></msup><mo>=</mo><mi>x</mi></mstyle></math> .

Take the <math><mstyle displaystyle="true"><mtext class="not-bold-word">(+2)th</mtext></mstyle></math> root of both sides of the <math><mstyle displaystyle="true"><mtext class="not-bold-word">equation</mtext></mstyle></math> to eliminate the exponent on the left side.

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

Simplify the right side of the equation.

Rewrite <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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

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

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the second solution.

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

Exclude the solutions that do not make <math><mstyle displaystyle="true"><msub><mi>log</mi><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mn>25</mn><mo>)</mo></mrow><mo>=</mo><mn>2</mn></mstyle></math> true.

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