If abcd = 100000000, then the value of <math><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>l</mi><mi>o</mi><msub><mrow><mi>g</mi></mrow><mrow><mi>a</mi></mrow></msub><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>l</mi><mi>o</mi><msub><mrow><mi>g</mi></mrow><mrow><mi>b</mi></mrow></msub><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>l</mi><mi>o</mi><msub><mrow><mi>g</mi></mrow><mrow><mi>c</mi></mrow></msub><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>l</mi><mi>o</mi><msub><mrow><mi>g</mi></mrow><mrow><mi>d</mi></mrow></msub><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math> is.

12loga10+12logb10+12logc10+12logd10=log10a2+log10b2+log10c2+log10d2=log10a+log10b+log10c+log10d2=log10abcd2=log101082=8 * ½ = 4

If abcd = 100000000, then the value of&nbsp;<math><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>l</mi><mi>o</mi><msub><mrow><mi>g</mi></mrow><mrow><mi>a</mi></mrow></msub><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>l</mi><mi>o</mi><msub><mrow><mi>g</mi></mrow><mrow><mi>b</mi></mrow></msub><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>l</mi><mi>o</mi><msub><mrow><mi>g</mi></mrow><mrow><mi>c</mi></mrow></msub><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>l</mi><mi>o</mi><msub><mrow><mi>g</mi></mrow><mrow><mi>d</mi></mrow></msub><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math>&nbsp;is.

None of these

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Option 1 -

Option 2 -

Option 3 -

Option 4 -

None of these

2 Views | Posted a month ago

Answered by

Payal Gupta | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

$\frac{1}{2 l o g_{a} 10} + \frac{1}{2 l o g_{b} 10} + \frac{1}{2 l o g_{c} 10} + \frac{1}{2 l o g_{d} 10}$

$= \frac{l o g_{10} a}{2} + \frac{l o g_{10} b}{2} + \frac{l o g_{10} c}{2} + \frac{l o g_{10} d}{2}$

$= \frac{l o g_{10} a + l o g_{10} b + l o g_{10} c + l o g_{10} d}{2}$

$= \frac{l o g_{10} a b c d}{2}$

$= \frac{l o g_{10} 1 0^{8}}{2}$

=8 * ½ = 4

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