Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 4*x=0
-
Equation 7*x=0
-
Equation 4x+3(x-7)=5
-
Equation x^2+6=5x
- Express {x} in terms of y where:
- 14*x-17*y=-4
- 18*x-10*y=-9
- 6*x+16*y=-7
- 2*x-16*y=14
- Derivative of:
-
3^x
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-3
- Integral of d{x}:
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3^x
-
-3
- Graphing y =:
- 3^x
- Sum of series:
-
-3
-
Identical expressions
- three ^x=- three
- 3 to the power of x equally minus 3
- three to the power of x equally minus three
- 3x=-3
-
Similar expressions
- 3^x=+3
3^x=-3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$3^{x} = -3$$
or
$$3^{x} + 3 = 0$$
or
$$3^{x} = -3$$
or
$$3^{x} = -3$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v + 3 = 0$$
or
$$v + 3 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = -3$$
We get the answer: v = -3
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(-3 \right)}}{\log{\left(3 \right)}} = 1 + \frac{i \pi}{\log{\left(3 \right)}}$$
$$3^{x} = -3$$
or
$$3^{x} + 3 = 0$$
or
$$3^{x} = -3$$
or
$$3^{x} = -3$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v + 3 = 0$$
or
$$v + 3 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = -3$$
We get the answer: v = -3
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(-3 \right)}}{\log{\left(3 \right)}} = 1 + \frac{i \pi}{\log{\left(3 \right)}}$$
Rapid solution
[src]
pi*I
x1 = 1 + ------
log(3)
$$x_{1} = 1 + \frac{i \pi}{\log{\left(3 \right)}}$$
x1 = 1 + i*pi/log(3)
Sum and product of roots
[src]
sum
pi*I
1 + ------
log(3)
$$1 + \frac{i \pi}{\log{\left(3 \right)}}$$
=
pi*I
1 + ------
log(3)
$$1 + \frac{i \pi}{\log{\left(3 \right)}}$$
product
pi*I
1 + ------
log(3)
$$1 + \frac{i \pi}{\log{\left(3 \right)}}$$
=
pi*I
1 + ------
log(3)
$$1 + \frac{i \pi}{\log{\left(3 \right)}}$$
1 + pi*i/log(3)
The graph