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प्रश्न
Given : `log x/ log y = 3/2` and log (xy) = 5; find the value of x and y.
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उत्तर
`log x/ log y = 3/2`
⇒ 2log x = 3log y
⇒ log y = `(2log x)/3` ...(1)
log( xy ) = 5
⇒ log x + log y = 5
⇒ log x + `(2log x)/3` = 5 ....[ Substituting (1) ]
⇒ `[ 3log x + 2log x ]/3 = 5`
⇒ `(5logx)/3 = 5`
⇒ log x = 3
⇒ x = 103
∴ x = 1000
Substituting x = 1000
log y = `[ 2 xx 3 ]/3`
⇒ log y = 2
⇒ y = 102
∴ y = 100.
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