Solve `x^((log)_y x)=2a n dy^((log)_x y)=16`

Consider equations x^(log_(y)x) = 2 and y^(log_(x)y) = 16 . The value of x is

The area bounded by the curves y=(log)_e xa n dy=((log)_e x)^2 is

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............

The x , y , z are positive real numbers such that (log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3, then the value of (1/(2z)) is ............

Find the area bounded by y=-(log)_e x , y=(log)_e x ,y=(log)_e(-x),a n dy=-(log)_e(-x)dot

Solve: log(1+(dy)/(dx))=x + y

Given system of simultaneous equations 2^x\ . 5^y=1\ a n d\ 5^(x+1). 2^y=2. Then - (a) . x=(log)_(10)5\ a n d\ y=(log)_(10)2 (b) . x=(log)_(10)2\ a n d\ y=(log)_(10)5 (c) . x=(log)_(10)(1/5)\ a n d\ y=(log)_(10)2 (d) . x=(log)_(10)5\ a n d\ y=(log)_(10)(1/2)

Find the area bounded by (a) y = (log)_e|x|a n dy=0 (b) y=|(log)_e|x||a n dy=0

If y=(log)_a x , find (dy)/(dx) .

find dy/dx if x y-(log y)=1