Question

Given : `log x/ log y = 3/2` and log (xy) = 5; find the value of x and y.

Answer 1

`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.