If the graphs of the functions`y= log _(e)x and y = ax` intersect at exactly two points,then find the value of `a`.

The graph y=2x^(3)-4x+2 and y=x^(3)+2x-1 intersect in exactly 3 distinct points.Then find the slope of the line passing through two of these points.

Find the range of function y=ln(2 x-x^(2))

Given the graphs of the two functions, y= f(x) & y =g(x). In theadjacent figure from point A on the graph of the function y fx)corresponding to the given value of the independent variable (say x),a straight line is drawn parallel to the X-axis to intersect the bisectorof the first and the third quadrants at point B. From the point B astraight line parallel to the Y-axis is drawn to intersect the graph ofthe function y= g(x) at C. Again a straight line is drawn from the point C parallel to the X-axis, to intersect the line NN' at D. If thestraight line NN' is parallel to Y-axis, then the co-ordinates of the point D are

If the graph of the function y=f(x) has a unique tangent at the point (a,0) through which the graph passes,then evaluate lim_(x rarr a)(log_(e){1+6f(x)})/(3f(x))

In the given figure, the two lines AB and CD intersect at a point O such that angleBOC=125^(@) . Find the values of x, y, and z.

For what values of a the graphs of the functions y=2ax+1 and y=(a-6)x^(2)-2 not intersect?

Draw the graph of the function y= 3x and from the graph , find the value of y, when x=4

Draw the graph of y= x ^((1)/(log_(e)x)) .

A line x=k intersects the graph of y=log_(4)x and y=log_(4)(x+4). The distance between the points of intersection is 0.5, then the value of k is

Draw the graph of y=log_(e)3x and compare with y=log_(e)x .