Advertisements
Advertisements
प्रश्न
Given : `log x/ log y = 3/2` and log (xy) = 5; find the value of x and y.
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.
APPEARS IN
संबंधित प्रश्न
If log`( a - b )/2 = 1/2( log a + log b )`, Show that : a2 + b2 = 6ab.
If log2(x + y) = log3(x - y) = `log 25/log 0.2`, find the values of x and y.
Evaluate: logb a × logc b × loga c.
Solve : log5( x + 1 ) - 1 = 1 + log5( x - 1 ).
Solve the following:
log (3 - x) - log (x - 3) = 1
Solve the following:
log(x2 + 36) - 2log x = 1
If log x = a and log y = b, write down
102b in terms of y
If x + log 4 + 2 log 5 + 3 log 3 + 2 log 2 = log 108, find the value of x.
Prove that (log a)2 - (log b)2 = `"log"("a"/"b")."log"("ab")`
If `"a" = "log""p"^2/"qr", "b" = "log""q"^2/"rp", "c" = "log""r"^2/"pq"`, find the value of a + b + c.
