Is it true that `x=e^(logx)` for all real

Is it true that x=e^(log x) for all real

e^(x+2logx)

Integrate e^(-logx)/ x

Let p(x)= x^2+ax+b have two distinct real roots, where a, b are real numbers. Define g(x)= p(x^3) for all real numbers x. Then which of the following statements are true? I. g has exactly two distinct real roots. II. g can have more than two distinct real roots III. There exists a real number alpha such that g(x) ge alpha for all real x

Let F(x) be an indefinite integral of sin^(2)x Statement-1: The function F(x) satisfies F(x+pi)=F(x) for all real x. because Statement-2: sin^(3)(x+pi)=sin^(2)x for all real x. A) Statement-1: True , statement-2 is true, Statement -2 is not a correct explanation for statement -1 c) Statement-1 is True, Statement -2 is False. D) Statement-1 is False, Statement-2 is True.

For the function y=f(x)=(x^2+b x+c)e^x , which of the following holds? (a) if f(x)>0 for all real x f'(x)>0 (a) if f(x)>0 for all real x=>f'(x)>0 (c) if f'(x)>0 for all real x=>f(x)>0 (d) if f'(x)>0 for all real x f(x)>0

If a,b,c are distinct positive numbers,then the nature of roots of the equation 1/(x-a)+1/(x-b)+1/(x-c)=1/x is a.all real real and is distinct b.all real and at leat two are distinct c.at least two real d.all non-real

If x^(y)=e^(x-y) then prove that (dy)/(dx)=(logx)/((1+logx)^(2))