Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 6-5(4x-1)=3
-
Equation x^2+4x-21=0
-
Equation x+5=7
-
Equation 6*x+2=-1
- Express {x} in terms of y where:
- -3*x-19*y=-9
- 3*x-11*y=20
- -17*x+16*y=-19
- -19*x+10*y=-3
- Graphing y =:
- e^x
- Derivative of:
-
e^x
- Integral of d{x}:
-
e^x
-
Identical expressions
- e^x= three
- e to the power of x equally 3
- e to the power of x equally three
- ex=3
e^x=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$e^{x} = 3$$
or
$$e^{x} - 3 = 0$$
or
$$e^{x} = 3$$
or
$$e^{x} = 3$$
- this is the simplest exponential equation
Do replacement
$$v = e^{x}$$
we get
$$v - 3 = 0$$
or
$$v - 3 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 3$$
We get the answer: v = 3
do backward replacement
$$e^{x} = v$$
or
$$x = \log{\left(v \right)}$$
The final answer
$$x_{1} = \frac{\log{\left(3 \right)}}{\log{\left(e \right)}} = \log{\left(3 \right)}$$
$$e^{x} = 3$$
or
$$e^{x} - 3 = 0$$
or
$$e^{x} = 3$$
or
$$e^{x} = 3$$
- this is the simplest exponential equation
Do replacement
$$v = e^{x}$$
we get
$$v - 3 = 0$$
or
$$v - 3 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 3$$
We get the answer: v = 3
do backward replacement
$$e^{x} = v$$
or
$$x = \log{\left(v \right)}$$
The final answer
$$x_{1} = \frac{\log{\left(3 \right)}}{\log{\left(e \right)}} = \log{\left(3 \right)}$$
Sum and product of roots
[src]
sum
log(3)
$$\log{\left(3 \right)}$$
=
log(3)
$$\log{\left(3 \right)}$$
product
log(3)
$$\log{\left(3 \right)}$$
=
log(3)
$$\log{\left(3 \right)}$$
log(3)
The graph