Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2-x-7=0
-
Equation 141*10^(-6)*x*3*sqrt(2)=sqrt((1-19881*10^(-12)*x^2)^2+9)
-
Equation e^x=4
-
Equation x^3=x^2-7x+7
- Express {x} in terms of y where:
- -6*x-13*y=17
- -7*x+5*y=1
- -6*x-19*y=7
- -19*x-4*y=-19
- Derivative of:
-
e^x
- Integral of d{x}:
-
e^x
- Graphing y =:
- e^x
-
Identical expressions
- e^x= four
- e to the power of x equally 4
- e to the power of x equally four
- ex=4
e^x=4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$e^{x} = 4$$
or
$$e^{x} - 4 = 0$$
or
$$e^{x} = 4$$
or
$$e^{x} = 4$$
- this is the simplest exponential equation
Do replacement
$$v = e^{x}$$
we get
$$v - 4 = 0$$
or
$$v - 4 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 4$$
We get the answer: v = 4
do backward replacement
$$e^{x} = v$$
or
$$x = \log{\left(v \right)}$$
The final answer
$$x_{1} = \frac{\log{\left(4 \right)}}{\log{\left(e \right)}} = \log{\left(4 \right)}$$
$$e^{x} = 4$$
or
$$e^{x} - 4 = 0$$
or
$$e^{x} = 4$$
or
$$e^{x} = 4$$
- this is the simplest exponential equation
Do replacement
$$v = e^{x}$$
we get
$$v - 4 = 0$$
or
$$v - 4 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 4$$
We get the answer: v = 4
do backward replacement
$$e^{x} = v$$
or
$$x = \log{\left(v \right)}$$
The final answer
$$x_{1} = \frac{\log{\left(4 \right)}}{\log{\left(e \right)}} = \log{\left(4 \right)}$$
Sum and product of roots
[src]
sum
log(4)
$$\log{\left(4 \right)}$$
=
log(4)
$$\log{\left(4 \right)}$$
product
log(4)
$$\log{\left(4 \right)}$$
=
log(4)
$$\log{\left(4 \right)}$$
log(4)
The graph