If \( \frac{1}{\log_2 x} + \frac{1}{\log_3 x} + \frac{1}{\log_4 x} + \frac{1}{\log_5 x} + \frac{1}{\log_6 x} = 1 \), then the value of \( x \) is
Show Hint
- 18
- 36
- 120
- 360
- 720
The Correct Option is
Solution and Explanation
Step 1: Use the property of logarithms \( \frac{1}{\log_b x} = \log_x b \).
This simplifies the given equation to: \[ \log_x 2 + \log_x 3 + \log_x 4 + \log_x 5 + \log_x 6 = 1 \] Simplifying the sum gives: \[ \log_x (2 \times 3 \times 4 \times 5 \times 6) = \log_x 720 \] Thus, \( x = 720 \).
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