Introduction to sample e learning:-
Sample e learning is important for students. Student’s does learning the sample e learning and also solve the e learning problems. 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,
`17e^x` this is a way to write an exponential function.
e = 2.718 is the value of e.
Basic Properties of Sample E Learning:-
In the following basic properties of sample e learning:
`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 `
Example Problems to Sample E Learning:-
Problem 1:-
Solve the exponential function equation `e^x = 47`
Solution:-
Here the natural log is the inverses of exponential function, so use ln to get fast solve this problem.
ln `e^x` = ln 47
x = ln 47 (take natural log of 47)
= 3.850
So the answer is 3.850
Problem 2:-
Solving add the exponential equation `e^(18x) +e^(11x)`
Solution:
Given: `e^(18x) +e^(11x)`
We know the property `e^x e^y = e^(x+y)`
Take the common term e.
= `e^(18x+11x)`
= `e^(29x)`
Adding the both values and get 29x.
Finally we get an answer as `e^(29x)`
Problem 3:-
Solving whether the point (0, 1) lies on the graph of the function y = 18(4)x.
Solution:-
Substitute x = 0 in the function y = 18(4)x.
We know the property `e^x`
y = 18(4)0
= 18(1)
= 18
The y–coordinate of the point is 1, which does not match with the obtained value y = 18.
So, the graph of the function y = 18(4)x does not contain the point (0, 1).
Sample e learning is important for students. Student’s does learning the sample e learning and also solve the e learning problems. 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,
`17e^x` this is a way to write an exponential function.
e = 2.718 is the value of e.
Basic Properties of Sample E Learning:-
In the following basic properties of sample e learning:
`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 `
Example Problems to Sample E Learning:-
Problem 1:-
Solve the exponential function equation `e^x = 47`
Solution:-
Here the natural log is the inverses of exponential function, so use ln to get fast solve this problem.
ln `e^x` = ln 47
x = ln 47 (take natural log of 47)
= 3.850
So the answer is 3.850
Problem 2:-
Solving add the exponential equation `e^(18x) +e^(11x)`
Solution:
Given: `e^(18x) +e^(11x)`
We know the property `e^x e^y = e^(x+y)`
Take the common term e.
= `e^(18x+11x)`
= `e^(29x)`
Adding the both values and get 29x.
Finally we get an answer as `e^(29x)`
Problem 3:-
Solving whether the point (0, 1) lies on the graph of the function y = 18(4)x.
Solution:-
Substitute x = 0 in the function y = 18(4)x.
We know the property `e^x`
y = 18(4)0
= 18(1)
= 18
The y–coordinate of the point is 1, which does not match with the obtained value y = 18.
So, the graph of the function y = 18(4)x does not contain the point (0, 1).
