**Introduction to definition of e tutoring:-**

Definition of e tutoring is the new way for the students. Tutor comes online to teach
the definition of e. Here e means e^x. In math exponential function means e^{x}, where e is the significance of e^{x} the same value again consequent.

For example,

`2e^x` this is a way to write an exponential function.

e = 2.718 is the value of e. Students does learn the exponential function definition, properties and rules. Because it is more helpful for exam preparation.

In the following basic properties to definition of e tutoring

- `e^x e^y = e^(x+y)`
- `(e^x)^p = e^(px)`
- `(de^x)/(dx) = e^x`
- `(de^ax)/(dx) = ae^(ax)`
- `(d^n e^ax)/(dx^n) = a^n e^(ax)`
- `e^x/ e^y = e^(x-y)`
- `root(p)(e^x) = e^(x/p)`
- `inte^x dx = e^x `

**Problem 1:-**

**Solving whether the point (0, 1) lies on the graph of the function y = 12(6)^{x}.**

**Solution:-**

Substitute *x* = 0 in the function *y* = 12(6)* ^{x}*.

We know the property `e^x`

*y* = 12(6)^{0}

= 12(1)

= 12

The *y*–coordinate of the point is 1, which does not match with the obtained value *y* = 12.

So, the graph of the function *y* = 12(6)* ^{x}* does not contain the point (0, 1).

**Problem 2:-**

**Solving the exponential function equation `e^x` = 35
Solution:-**

Here the natural log is the inverses of exponential function, so use ln to get fast solve this problem.

ln `e^x` = ln 35

x = ln 35 (take natural log of 35)

= 3.555

So the answer is 3.555

**Problem 3:-**

**Solving add the exponential equation `e^(13x) +e^(6x)`**

**Solution:**

Given: `e^(13x) +e^(6x)`

We know the property `e^x e^y = e^(x+y)`

Take the common term e.

= `e^(13x+6x)`

= `e^(19x)`

Adding the both values and get 19x.

Finally we get an answer as `e^(19x)`