Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^3-3*x^2-8*x+24=0
-
Equation log(3*x)=3
-
Equation 2x=-3
-
Equation x-1/3=210
- Express {x} in terms of y where:
- -12*x+10*y=2
- 1*x-17*y=10
- 10*x+7*y=-8
- -8*x+11*y=-8
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Identical expressions
- e^(-z)+ one = zero
- e to the power of ( minus z) plus 1 equally 0
- e to the power of ( minus z) plus one equally zero
- e(-z)+1=0
- e-z+1=0
- e^-z+1=0
- e^(-z)+1=O
-
Similar expressions
- e^(z)+1=0
- e^(-z)-1=0
e^(-z)+1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$1 + e^{- z} = 0$$
or
$$1 + e^{- z} = 0$$
or
$$e^{- z} = -1$$
or
$$e^{- z} = -1$$
- this is the simplest exponential equation
Do replacement
$$v = e^{- z}$$
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
$$e^{- z} = v$$
or
$$z = - \log{\left(v \right)}$$
The final answer
$$z_{1} = \frac{\log{\left(-1 \right)}}{\log{\left(e^{-1} \right)}} = - i \pi$$
$$1 + e^{- z} = 0$$
or
$$1 + e^{- z} = 0$$
or
$$e^{- z} = -1$$
or
$$e^{- z} = -1$$
- this is the simplest exponential equation
Do replacement
$$v = e^{- z}$$
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
$$e^{- z} = v$$
or
$$z = - \log{\left(v \right)}$$
The final answer
$$z_{1} = \frac{\log{\left(-1 \right)}}{\log{\left(e^{-1} \right)}} = - i \pi$$
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