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Question

যদি $\log (\frac{a}{b}) + \log (\frac{b}{a}) = \log (a + b)$ হয় তবে -

a + b = 1

a - b = 1

a = b

a^{2} - b^{2} = 1

ANSWER : 1

Descrption

<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>log</mi><mfenced><mfrac><mi>a</mi><mi>b</mi></mfrac></mfenced><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>log</mi><mfenced><mfrac><mi>b</mi><mi>a</mi></mfrac></mfenced><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>log</mi><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mspace linebreak="newline">&nbsp;</mspace><mi>log</mi><mfenced><mrow><mfrac><mi>a</mi><mi>b</mi></mfrac><mo>×</mo><mfrac><mi>b</mi><mi>a</mi></mfrac></mrow></mfenced><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mi>log</mi><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mspace linebreak="newline">&nbsp;</mspace><mo>&nbsp;</mo><mi>log</mi><mfenced><mn>1</mn></mfenced><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mi>log</mi><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mspace linebreak="newline">&nbsp;</mspace><mn>1</mn><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>[</mo><mi>E</mi><mi>l</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>n</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>n</mi><mi>g</mi><mo>&nbsp;</mo><mi>log</mi><mo>&nbsp;</mo><mi>f</mi><mi>r</mi><mi>o</mi><mi>m</mi><mo>&nbsp;</mo><mi>b</mi><mi>o</mi><mi>t</mi><mi>h</mi><mo>&nbsp;</mo><mi>s</mi><mi>i</mi><mi>d</mi><mi>e</mi><mi>s</mi><mo>]</mo><mspace linebreak="newline">&nbsp;</mspace><mi mathvariant="bold-italic">a</mi><mo mathvariant="bold">+</mo><mi mathvariant="bold-italic">b</mi><mo mathvariant="bold">&nbsp;</mo><mo mathvariant="bold">=</mo><mo mathvariant="bold">&nbsp;</mo><mn mathvariant="bold">1</mn><mo mathvariant="bold">&nbsp;</mo><mo mathvariant="bold">(</mo><mi mathvariant="bold-italic">A</mi><mi mathvariant="bold-italic">n</mi><mi mathvariant="bold-italic">s</mi><mo mathvariant="bold">)</mo></math></p>

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