Advertisements
Advertisements
प्रश्न
If a = `"log" 3/5, "b" = "log" 5/4 and "c" = 2 "log" sqrt(3/4`, prove that 5a+b-c = 1
Advertisements
उत्तर
Consider `"log"(5^("a"+"b"-"c"))`
= (a + b - c)log5
= `("log"3/5 + "log"5/4 -2"log"sqrt(3/4))"log"5`
= `("log"3/5 + "log"5/4 - "log"[sqrt(3/4)]^2)"log"5`
= `("log"3/5 + "log"5/4 - "log"3/4)"log"5`
= `"log"((3/5 xx 5/4)/(3/4))"log"5`
= log1 x log5 = 0 ...[∵ log1 = 0]
∴ `5^("a"+ "b"-"c")`
= 10°
= 1.
APPEARS IN
संबंधित प्रश्न
If log`( a - b )/2 = 1/2( log a + log b )`, Show that : a2 + b2 = 6ab.
If a2 + b2 = 23ab, show that:
log `(a + b)/5 = 1/2`(log a + log b).
Solve the following:
log (3 - x) - log (x - 3) = 1
Solve the following:
log 4 x + log 4 (x-6) = 2
Solve the following:
log 8 (x2 - 1) - log 8 (3x + 9) = 0
If log x = a and log y = b, write down
102b in terms of y
If log 3 m = x and log 3 n = y, write down
32x-3 in terms of m
If 2 log x + 1 = log 360, find: log (3 x2 - 8)
Prove that (log a)2 - (log b)2 = `"log"("a"/"b")."log"("ab")`
Prove that log 10 125 = 3 (1 - log 10 2)
