For logarithmic equations, <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> such that <math><mstyle displaystyle="true"><mi>x</mi><mo>></mo><mn>0</mn></mstyle></math> , <math><mstyle displaystyle="true"><mi>b</mi><mo>></mo><mn>0</mn></mstyle></math> , and <math><mstyle displaystyle="true"><mi>b</mi><mo>≠</mo><mn>1</mn></mstyle></math> . In this case, <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>3</mn></mstyle></math> , <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mi>x</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mn>2</mn></mstyle></math> .

Substitute the values of <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> , <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> , and <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> into the equation <math><mstyle displaystyle="true"><msup><mrow><mi>b</mi></mrow><mrow><mi>y</mi></mrow></msup><mo>=</mo><mi>x</mi></mstyle></math> .

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