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The value of log4 3 × log5 4 x … x log9 8 × log3 9 is _______.
  • a)
    1
  • b)
    2
  • c)
    1/2
  • d)
    1/3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The value of log4 3 × log5 4 x … x log9 8 × log3 9 ...
Explanation:
To find the value of the given expression, we need to simplify it step by step by applying the rules of logarithms.

Step 1: Simplify each term
- log4 3 = log3 / log4 = 1 / log4
- log5 4 = log4 / log5 = 1 / log5
- log9 8 = log8 / log9 = 1 / log9

Step 2: Substitute the simplified terms back into the expression
log4 3 * log5 4 * ... * log9 8 = (1 / log4) * (1 / log5) * ... * (1 / log9)

Step 3: Combine the terms using the property loga + logb = log(ab)
= 1 / (log4 * log5 * ... * log9)

Step 4: Simplify the expression further
= 1 / (log3)

Step 5: Final answer
= 1
Therefore, the value of log4 3 * log5 4 * ... * log9 8 is 1.
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