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प्रश्न
Given `log_x 25 - log_x 5 = 2 - log_x (1/125)` ; find x.
उत्तर
`log_x 25 - log_x 5 = 2 - log_x (1/125)`
⇒ `log_x 5^2 - log_x 5 = 2 - log_x (1/5)^3`
⇒ `log_x 5^2 - log_x 5 = 2 - log_x 5^-3`
⇒ `2log_x 5 - log_x 5 = 2 + 3log_x 5`
⇒ `2log_x 5 - log_x 5 - 3log_x 5 = 2`
⇒ - 2logx5 = 2
⇒ logx5 = -1
⇒ x-1 = 5
⇒ `1/x` = 5
⇒ x = `1/5`.
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