# Definition of E Tutoring

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 ex, where e is the significance of ex 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.

## Basic Properties to Definition of E Tutoring:-

In the following basic properties to definition of e tutoring

1. `e^x e^y = e^(x+y)`
2. `(e^x)^p = e^(px)`
3. `(de^x)/(dx) = e^x`
4. `(de^ax)/(dx) = ae^(ax)`
5. `(d^n e^ax)/(dx^n) = a^n e^(ax)`
6. `e^x/ e^y = e^(x-y)`
7. `root(p)(e^x) = e^(x/p)`
8. `inte^x dx = e^x `

## Example Problems to Definition of E Tutoring:-

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

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)`