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for x > 1 if (2x)^(2y)=4e^(2x-2y) then (...

for `x > 1` if `(2x)^(2y)=4e^(2x-2y)` then `(1+log_e 2x)^2 (dy)/(dx)`

A

`(x log_e 2x+log_e 2)/(x)`

B

`log_e 2x`

C

`(xlog_e 2x-log_e 2)/(x)`

D

`x log_e 2x`.

Text Solution

Verified by Experts

The correct Answer is:
C
`(2x)^(2y)=4e^(2x-2y)`
Taking log both sides `yl n(2n)=2 ln 2+2(x-y)`.
`rArr y=(ln 2+x)/(1+ln2x)`. `(dy)/(dx)=((1+ln2x)(1)-(ln2+x)(1)/(x))/((1+ln2x)^2)`
So, `(1+ln2x)^2 (dy)/(dx)=(xln(2n)-ln2)/(x)`.
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