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`

The area bounded by the curve y=2^(x), the x- axis and the left of y-axis is (A) log _(e)2(B)log_(e)4 (C) log_(4)e(D)log_(2)e

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

If A is the area of the figure bounded by the straight lines x = 0 and x = 2 and the curves y = 2x and y=2x-x^(2) then the value of ((3)/(log2)-A) is

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.

" The area of the bounded region ",{(x,y):xy<=8,1<=y<=x^(2)}" is ",[[" (A) ",8log_(e)2-(14)/(3)],[" (B) ",16log_(e)2-(14)/(3)],[" (c) ",16log_(e)2-6],[" (D) ",8log_(e)2-(7)/(3)]]

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

Solve for x: log_(4) log_(3) log_(2) x = 0 .

The number of solution of log_4(x-1)=log_2(x-3) is (A) 3 (B) 5 (C) 2 (D) 0

Solve : (3)/(2)log_(4)(x+2)^(2)+3=log_(4)(4-x)^(3)+log_(4)(6+x)^(3) .