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CA Foundation doubt

If log((a+b)/3) = ½(log a + log b), what is the value of a/b + b/a?

Can anyone know the solution of 53

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Asked by Devanshi··2 answers

2 replies

  1. BrunoAI answerAI first answer — verify with your teacher

    Answer: (c) 7 1. RHS: 1/2(log a + log b) = log √(ab) 2. So (a+b)/3 = √(ab) 3. Square both sides: (a+b)² = 9ab, so a² + 2ab + b² = 9ab, giving a² + b² = 7ab 4. a/b + b/a = (a² + b²)/ab = 7ab/ab = 7 Bonus: Q54 uses the same identity (a² + b² = 7ab), so its expression comes out to 0.

  2. Veer

    1. Right side me log rule lagao: \(\frac{1}{2}(\log a + \log b)\) ban jayega \(\log(\sqrt{ab})\). 2. Dono taraf se \(\log \) hata do, toh bachega \(\frac{a+b}{3} = \sqrt{ab}\). 3. Ab dono side square karo, toh \((a+b)^2 = 9ab\) aa jayega. 4. Formula kholo: \(a^2 + b^2 + 2ab = 9ab\), yani \(a^2 + b^2 = 7ab\). 5. Bas ab poore equation ko \(ab\) se divide kar do, seedha \(\frac{a}{b} + \frac{b}{a} = 7\) mil jayega

Related questions

What is the product rule of logarithms?

The log of a product equals the sum of the logs: log(mn) = log m + log n, for positive m and n.

Why can we remove log from both sides of an equation?

The log function is one-to-one for positive numbers, so if log x = log y then x = y.

How is a/b + b/a written in terms of a and b?

a/b + b/a = (a² + b²)/ab, which is why finding a² + b² in terms of ab gives the answer directly.

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