Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+2x+1=0
-
Equation cos(x/2)=1/2
-
Equation (x+7)*(x-1)=0
-
Equation -4/7*x^2+28=0
- Express {x} in terms of y where:
- -17*x+14*y=11
- -1*x-17*y=10
- 3*x+3*y=10
- 12*x+12*y=-3
- Derivative of:
-
e^x
- Graphing y =:
- e^x
- Integral of d{x}:
-
e^x
-
Identical expressions
- e^x= two
- e to the power of x equally 2
- e to the power of x equally two
- ex=2
e^x=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$e^{x} = 2$$
or
$$e^{x} - 2 = 0$$
or
$$e^{x} = 2$$
or
$$e^{x} = 2$$
- this is the simplest exponential equation
Do replacement
$$v = e^{x}$$
we get
$$v - 2 = 0$$
or
$$v - 2 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 2$$
We get the answer: v = 2
do backward replacement
$$e^{x} = v$$
or
$$x = \log{\left(v \right)}$$
The final answer
$$x_{1} = \frac{\log{\left(2 \right)}}{\log{\left(e \right)}} = \log{\left(2 \right)}$$
$$e^{x} = 2$$
or
$$e^{x} - 2 = 0$$
or
$$e^{x} = 2$$
or
$$e^{x} = 2$$
- this is the simplest exponential equation
Do replacement
$$v = e^{x}$$
we get
$$v - 2 = 0$$
or
$$v - 2 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 2$$
We get the answer: v = 2
do backward replacement
$$e^{x} = v$$
or
$$x = \log{\left(v \right)}$$
The final answer
$$x_{1} = \frac{\log{\left(2 \right)}}{\log{\left(e \right)}} = \log{\left(2 \right)}$$
Sum and product of roots
[src]
sum
log(2)
$$\log{\left(2 \right)}$$
=
log(2)
$$\log{\left(2 \right)}$$
product
log(2)
$$\log{\left(2 \right)}$$
=
log(2)
$$\log{\left(2 \right)}$$
log(2)
The graph