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Question

\log_{x} \frac{9}{16} = - \frac{1}{2}

, the value of the base is -

16/9

9/16

256/81

81/256

ANSWER : 3

Descrption

<pre>
Given, 
<math xmlns = "http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mi>x</mi></msub><mfrac><mn>9</mn><mn>16</mn></mfrac><mo> = </mo><mo> - </mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mspace linebreak = "newline"/><mo>&#x21D2;</mo><msup><mi>x</mi><mrow><mo> - </mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></msup><mo> = </mo><mfrac><mn>9</mn><mn>16</mn></mfrac><mspace linebreak = "newline"/><mo>&#x21D2;</mo><mfrac><mn>1</mn><mstyle displaystyle = "true"><mfrac><mn>1</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></mstyle></mfrac><mo> = </mo><mfrac><mn>9</mn><mn>16</mn></mfrac><mspace linebreak = "newline"/><mo>&#x21D2;</mo><msup><mi>x</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><mo> = </mo><mfrac><mn>16</mn><mn>9</mn></mfrac><mspace linebreak = "newline"/><mo>&#x21D2;</mo><mo>(</mo><msup><mi>x</mi><mfrac><mn>1</mn><mn>2</mn></mfrac></msup><msup><mo>)</mo><mn>2</mn></msup><mo> = </mo><mo>(</mo><mfrac><mn>16</mn><mn>9</mn></mfrac><msup><mo>)</mo><mn>2</mn></msup><mspace linebreak = "newline"/><mo>&#x21D2;</mo><msup><mi>x</mi><mfrac><mn>2</mn><mn>2</mn></mfrac></msup><mo> = </mo><mfrac><mn>256</mn><mn>81</mn></mfrac><mspace linebreak = "newline"/><mo>.</mo><mo>'</mo><mo>.</mo><mo>&#xA0;</mo><mi>x</mi><mo> = </mo><mfrac><mn>256</mn><mn>81</mn></mfrac></math>
</pre>

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