Home
Class 12
MATHS
If y= 2^((1)/(log(x)4)) then prove that ...

If y= `2^((1)/(log_(x)4))` then prove that `x=y^(2)`.

Text Solution

Verified by Experts

`2^((1)/(log_(x)4))`
`:." "y=2^(log_(4)x)" "rArry=2^((1)/(2)log_(2)x)`
`rArr y^(2) = 2^(log_(2)x)" "("as "y gt 0)`
` rArr y^(2) = x `
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.1|6 Videos
  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.2|9 Videos
  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos
  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

If y = a^(1/(1-log_(a) x)) and z = a^(1/(1-log_(a)y))",then prove that "x=a^(1/(1-log_(a)z))

If y=a^(x^(a^x..oo)) then prove that dy/dx=(y^2 log y )/(x(1-y log x log y))

If (log x)/(y-z)=(log y)/(z-x)=(log z)/(x-y), then prove that: x^(x)y^(y)z^(z)=1

y=[log(x+sqrt(x^(2)+1))]^(2) then prove that (x^(2)+1)y_(2)+xy_(1)=2

If y=a^x^a^x^...^(((((oo))))) , then prove that (dy)/(dx)=(y^2(log)_e y)/(x(1-y(log)_e x(log)_e y)

If y=a^(x^(x^(2)*oo)), prove that (dy)/(dx)=(y^(2)log y)/(x(1-y log x*log y))

if x^(4) + y^(4) = 83 x^(2)y^(2) then prove that log((x^(2) -y^(2))/9) = logx + logy.

y=e^(x)log x then prove that xy_(2)-(2x-1)y_(1)+(x-1)y=0

If y=x^(n){a cos(log x)+b sin(log x)}, prove that x^(2)(d^(2)y)/(dx^(2))+(1-2n)(dy)/(dx)+(1+n^(2))y=0