#### To determine

**To find:**

The positive number a does the curve intersect the line.

**Solution:**eln|x|x.

#### Explanation

**Given:**

The expression of curve and line are y=ax and y=x respectively.

**Formulae used:**

Thes

ubstitution

Consider y=ax and y=x

Hence, use the formulae of substitution

Now according to the given expression, the value of *a* is

ax=xxlna=ln|x|lna=ln|x|xa=eln|x|x

At x=0 the value of a will touch the infinity hence x always greater than 0.

y=x is a straight line which passes through the origin point. Hence if x is not equal to zero then it will not intersect with the origin point.

Hence according to the a=eln|x|x

x is always greater than zero and

x∈(0,∞] where x is a real number.

The graph below clarifies the situation.

**Conclusion: **Hence the positive number a is eln|x|x