Area of the region bounded by the curves `y=2^x, y=2x-x^2, x=0` and `x=2` is given by (A) `3log2-4/3` (B) `3/log2-4/3` (C) `3log2+4/3` (D) `3/log2+4/3`

int_2^4 log[x]dx is (A) log2 (B) log3 (C) log5 (D) none of these

int_2^4 log[x]dx is (A) log2 (B) log3 (C) log5 (D) none of these

Statement 1: The area of the region bounded by the curve 2y=log_(e)x,y=e^(2x), and the pair of lines (x+y-1)x(x+y-3)=0 is 2k sq.units Statement 2: The area of the region bounded by the curves 2y=log_(e)x,y=e^(2x), and the pair of lines x^(2)+y^(2)+2xy-4x-4y+3=0 is k units.

Solve: log_2 (4/(x+3)) > log_2 (2-x)

The area bounded by the curves xsqrt3+y=2log_(e)(x-ysqrt3)-2log_(e)2, y=sqrt3x, y=-(1)/(sqrt3)x+2, is

The area bounded by the curves xsqrt3+y=2log_(e)(x-ysqrt3)-2log_(e)2, y=sqrt3x, y=-(1)/(sqrt3)x+2, is

The area bounded by the curves xsqrt3+y=2log_(e)(x-ysqrt3)-2log_(e)2, y=sqrt3x, y=-(1)/(sqrt3)x+2, is

Evaluate each of the following in terms of x and y, if it is given x=log_2^3 and y=log_2^5 . log_2^4.5

If 3^x=4^(x-1) , then x= (2(log)_3 2)/(2(log)_3 2-1) (b) 2/(2-(log)_2 3) 1/(1-(log)_4 3) (d) (2(log)_2 3)/(2(log)_2 3-1)

If 3^x=4^(x-1) , then x= (2(log)_3 2)/(2(log)_3 2-1) (b) 2/(2-(log)_2 3) 1/(1-(log)_4 3) (d) (2(log)_2 3)/(2(log)_2 3-1)