An algebra problem by prasanth pp
If
and
find the value of
:
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1 solution
Given e f ( x ) = ( 1 0 + x ) / ( 1 0 − x )
taking natural log on both sides..> f ( x ) = l n ( 1 0 + x ) / ( 1 0 − x )...............(1)
also given f ( x ) = k × f ( 2 0 0 x / ( 1 0 0 + x 2 ) ) ...............................(2)
equating both equations:
f ( x ) = l n ( 1 0 + x ) / ( 1 0 − x ) = k × l n ( 1 0 + 2 0 0 x / ( 1 0 0 + x 2 ) / 1 0 − 2 0 0 x / ( 1 0 0 + x 2 )
l n ( 1 0 + x ) / ( 1 0 − x ) = k × l n ( 1 0 x 2 + 2 0 0 x + 1 0 0 0 ) / ( 1 0 x 2 − 2 0 0 x + 1 0 0 0 )
l n ( 1 0 + x ) / ( 1 0 − x ) = k × l n ( x 2 + 2 0 x + 1 0 0 ) / ( x 2 − 2 0 x + 1 0 0 )
l n ( 1 0 + x ) / ( 1 0 − x ) = k × l n ( ( 1 0 + x ) / ( 1 0 − x ) ) 2
l n ( 1 0 + x ) / ( 1 0 − x ) = k × 2 l n ( 1 0 + x ) / ( 1 0 − x )
=>2*k=1
k=1/2
k=0.5