Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin(x)=0
-
Equation x^2=64
-
Equation z^3=1
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Equation 2^x=-1
- Express {x} in terms of y where:
- -7*x+19*y=-8
- 5*x+8*y=6
- 6*x+14*y=-7
- 3*x+6*y=16
- Derivative of:
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2^x
-
-1
- Integral of d{x}:
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2^x
-
-1
- Graphing y =:
- 2^x
- Sum of series:
-
-1
-
Identical expressions
- two ^x=- one
- 2 to the power of x equally minus 1
- two to the power of x equally minus one
- 2x=-1
-
Similar expressions
- 2^x=+1
2^x=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$2^{x} = -1$$
or
$$2^{x} + 1 = 0$$
or
$$2^{x} = -1$$
or
$$2^{x} = -1$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
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
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(-1 \right)}}{\log{\left(2 \right)}} = \frac{i \pi}{\log{\left(2 \right)}}$$
$$2^{x} = -1$$
or
$$2^{x} + 1 = 0$$
or
$$2^{x} = -1$$
or
$$2^{x} = -1$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
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
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(-1 \right)}}{\log{\left(2 \right)}} = \frac{i \pi}{\log{\left(2 \right)}}$$
Rapid solution
[src]
pi*I
x1 = ------
log(2)
$$x_{1} = \frac{i \pi}{\log{\left(2 \right)}}$$
x1 = i*pi/log(2)
Sum and product of roots
[src]
sum
pi*I ------ log(2)
$$\frac{i \pi}{\log{\left(2 \right)}}$$
=
pi*I ------ log(2)
$$\frac{i \pi}{\log{\left(2 \right)}}$$
product
pi*I ------ log(2)
$$\frac{i \pi}{\log{\left(2 \right)}}$$
=
pi*I ------ log(2)
$$\frac{i \pi}{\log{\left(2 \right)}}$$
pi*i/log(2)
The graph