Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation cos(x)-1=0
-
Equation x+5=7
-
Equation 16*x^3+8*x^2+x=0
-
Equation -7x=4
- Express {x} in terms of y where:
- 19*x+2*y=17
- 8*x-9*y=-1
- 13*x-1*y=-20
- 9*x+8*y=-4
- Derivative of:
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e^x+1
- Integral of d{x}:
-
e^x+1
-
Identical expressions
- e^x+ one = zero
- e to the power of x plus 1 equally 0
- e to the power of x plus one equally zero
- ex+1=0
- e^x+1=O
-
Similar expressions
- e^x-1=0
e^x+1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$e^{x} + 1 = 0$$
or
$$e^{x} + 1 = 0$$
or
$$e^{x} = -1$$
or
$$e^{x} = -1$$
- this is the simplest exponential equation
Do replacement
$$v = e^{x}$$
we get
$$v + 1 = 0$$
or
$$v + 1 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = -1$$
We get the answer: v = -1
do backward replacement
$$e^{x} = v$$
or
$$x = \log{\left(v \right)}$$
The final answer
$$x_{1} = \frac{\log{\left(-1 \right)}}{\log{\left(e \right)}} = i \pi$$
$$e^{x} + 1 = 0$$
or
$$e^{x} + 1 = 0$$
or
$$e^{x} = -1$$
or
$$e^{x} = -1$$
- this is the simplest exponential equation
Do replacement
$$v = e^{x}$$
we get
$$v + 1 = 0$$
or
$$v + 1 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = -1$$
We get the answer: v = -1
do backward replacement
$$e^{x} = v$$
or
$$x = \log{\left(v \right)}$$
The final answer
$$x_{1} = \frac{\log{\left(-1 \right)}}{\log{\left(e \right)}} = i \pi$$
Sum and product of roots
[src]
sum
pi*I
$$i \pi$$
=
pi*I
$$i \pi$$
product
pi*I
$$i \pi$$
=
pi*I
$$i \pi$$
pi*i
The graph