Home
Class 12
MATHS
Prove that the equation x^(log(sqrtx^(2x...

Prove that the equation `x^(log_(sqrtx^(2x)))=4` has no solution.

Text Solution

Verified by Experts

We have ` x^(log_(sqrtx^(2x)))=4, x gt 0 , x ne 1`
` rArr x ^(2 log_(x) 2x) = 4`
` rArr x^(log_(x)4x^(2))=4`
` rArr 4x^(2) = 4`
` rArr x = pm 1`,which is not possible.
Hence, equation has no solution.
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.5|13 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.6|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.3|16 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

Find the possible values of p such that the equation p x^2=(log)_e x has exactly one solution.

Find the possible values of p such that the equation p x^2=(log)_e x has exactly one solution.

Prove that the equation 2 sin x=|x|+a has no solution for a in ((3sqrt(3)-pi)/3, oo) .

A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=x has no real roots. Prove that in this case equation P(P(x))=x has no real roots either.

The solution set of the equation x^(log_x(1-x)^2)=9 is

consider the system of equations : ltbr. 3x-y +4z=3 x+2y-3z =-2 6x+5y+lambdaz =-3 Prove that system of equation has at least one solution for all real values of lambda .also prove that infinite solutions of the system of equations satisfy (7x-4)/(-5)=(7y+9)/(13)=z

The equation (ay-bx)^(2)+4xy=0 has rational solutions x , y for

Draw the graph of y= log_(x)sqrtx

If the equation x^(log_(a)x^(2))=(x^(k-2))/a^(k),a ne 0 has exactly one solution for x, then the value of k is/are

The equation sqrt(1+log_(x) sqrt27) log_(3) x+1 = 0 has