Advertisements
Advertisements
प्रश्न
Prove that : (log a)2 - (log b)2 = log `(( a )/( b ))` . Log (ab)
Advertisements
उत्तर
L.H.S = ( log a )2 - ( log b )2
⇒ L.H.S = ( log a + log b ) ( log a - log b )
⇒ L.H.S = log ( ab ) log `(( a )/( b ))`
⇒ L.H.S = log `(( a )/( b ))` x log ( ab)
⇒ L.H.S = R.H.S
Hence proved.
APPEARS IN
संबंधित प्रश्न
If log102 = a and log103 = b ; express each of the following in terms of 'a' and 'b': log 2.25
If log (a + 1) = log (4a - 3) - log 3; find a.
Given `log_x 25 - log_x 5 = 2 - log_x (1/125)` ; find x.
Express the following in terms of log 2 and log 3: log 144
Express the following in terms of log 5 and/or log 2: log80
Express the following in terms of log 5 and/or log 2: log500
Express the following as a single logarithm:
`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`
Express the following as a single logarithm:
`(1)/(2)"log"25 - 2"log"3 + "log"36`
Simplify the following:
`2 "log" 5 +"log" 8 - (1)/(2) "log" 4`
If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: `"log" sqrt(72)`
