Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 49*x^3+14*x^2+x=0
-
Equation 4^x=8
-
Equation x^2-x=12
-
Equation x-5(x+3)=5
- Express {x} in terms of y where:
- -7*x-13*y=-12
- -3*x+19*y=16
- -4*x+4*y=-9
- -19*x-2*y=-6
- Derivative of:
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3^x
-
-1
- Integral of d{x}:
-
3^x
-
-1
- Graphing y =:
- 3^x
- Sum of series:
-
-1
-
Identical expressions
- three ^x=- one
- 3 to the power of x equally minus 1
- three to the power of x equally minus one
- 3x=-1
-
Similar expressions
- 3^x=+1
3^x=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$3^{x} = -1$$
or
$$3^{x} + 1 = 0$$
or
$$3^{x} = -1$$
or
$$3^{x} = -1$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
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
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(-1 \right)}}{\log{\left(3 \right)}} = \frac{i \pi}{\log{\left(3 \right)}}$$
$$3^{x} = -1$$
or
$$3^{x} + 1 = 0$$
or
$$3^{x} = -1$$
or
$$3^{x} = -1$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
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
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(-1 \right)}}{\log{\left(3 \right)}} = \frac{i \pi}{\log{\left(3 \right)}}$$
Rapid solution
[src]
pi*I
x1 = ------
log(3)
$$x_{1} = \frac{i \pi}{\log{\left(3 \right)}}$$
x1 = i*pi/log(3)
Sum and product of roots
[src]
sum
pi*I ------ log(3)
$$\frac{i \pi}{\log{\left(3 \right)}}$$
=
pi*I ------ log(3)
$$\frac{i \pi}{\log{\left(3 \right)}}$$
product
pi*I ------ log(3)
$$\frac{i \pi}{\log{\left(3 \right)}}$$
=
pi*I ------ log(3)
$$\frac{i \pi}{\log{\left(3 \right)}}$$
pi*i/log(3)
The graph