Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2=5
-
Equation k^2+k=0
-
Equation 5x=0
-
Equation x^2-15=2x
- Express {x} in terms of y where:
- -4*x+3*y=9
- -2*x-19*y=-11
- -5*x+15*y=-15
- -1*x+7*y=-11
- Derivative of:
-
2^x
- -4
- Integral of d{x}:
-
2^x
-
-4
- Graphing y =:
- 2^x
- Limit of the function:
- -4
-
Identical expressions
- two ^x=- four
- 2 to the power of x equally minus 4
- two to the power of x equally minus four
- 2x=-4
-
Similar expressions
- 2^x=+4
2^x=-4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$2^{x} = -4$$
or
$$2^{x} + 4 = 0$$
or
$$2^{x} = -4$$
or
$$2^{x} = -4$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
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
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(-4 \right)}}{\log{\left(2 \right)}} = \frac{\log{\left(4 \right)} + i \pi}{\log{\left(2 \right)}}$$
$$2^{x} = -4$$
or
$$2^{x} + 4 = 0$$
or
$$2^{x} = -4$$
or
$$2^{x} = -4$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
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
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(-4 \right)}}{\log{\left(2 \right)}} = \frac{\log{\left(4 \right)} + i \pi}{\log{\left(2 \right)}}$$
Sum and product of roots
[src]
sum
log(4) pi*I ------ + ------ log(2) log(2)
$$\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}$$
=
log(4) pi*I ------ + ------ log(2) log(2)
$$\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}$$
product
log(4) pi*I ------ + ------ log(2) log(2)
$$\frac{\log{\left(4 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}$$
=
pi*I + log(4)
-------------
log(2)
$$\frac{\log{\left(4 \right)} + i \pi}{\log{\left(2 \right)}}$$
(pi*i + log(4))/log(2)
Rapid solution
[src]
log(4) pi*I
x1 = ------ + ------
log(2) log(2)
$$x_{1} = \frac{\log{\left(4 \right)}}{\log{\left(2 \right)}} + \frac{i \pi}{\log{\left(2 \right)}}$$
x1 = log(4)/log(2) + i*pi/log(2)
The graph