Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sinx=1
-
Equation cosx=1/2
-
Equation sqrt(x)+1=x-1
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Equation 5^x=-5
- Express {x} in terms of y where:
- xy^1=y+x*sin(y/x)
- sqrt(x)*sin(y/x)=0
- 12*10^(-30)-0,1884*10^12*x^2-y(0,3768*10^12*x+1,183152*10^12*x^3)+y^2(2,760688*10^24*x^2)=0=0
- (x^2+y^2)×(x+y-3)=2xy
- Integral of d{x}:
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5^x
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-5
- Derivative of:
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5^x
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-5
- Graphing y =:
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5^x
- -5
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Identical expressions
- five ^x=- five
- 5 to the power of x equally minus 5
- five to the power of x equally minus five
- 5x=-5
-
Similar expressions
- 5^x=+5
5^x=-5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$5^{x} = -5$$
or
$$5^{x} + 5 = 0$$
or
$$5^{x} = -5$$
or
$$5^{x} = -5$$
- this is the simplest exponential equation
Do replacement
$$v = 5^{x}$$
we get
$$v + 5 = 0$$
or
$$v + 5 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = -5$$
We get the answer: v = -5
do backward replacement
$$5^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(5 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(-5 \right)}}{\log{\left(5 \right)}} = 1 + \frac{i \pi}{\log{\left(5 \right)}}$$
$$5^{x} = -5$$
or
$$5^{x} + 5 = 0$$
or
$$5^{x} = -5$$
or
$$5^{x} = -5$$
- this is the simplest exponential equation
Do replacement
$$v = 5^{x}$$
we get
$$v + 5 = 0$$
or
$$v + 5 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = -5$$
We get the answer: v = -5
do backward replacement
$$5^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(5 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(-5 \right)}}{\log{\left(5 \right)}} = 1 + \frac{i \pi}{\log{\left(5 \right)}}$$
Sum and product of roots
[src]
sum
pi*I
1 + ------
log(5)
$$1 + \frac{i \pi}{\log{\left(5 \right)}}$$
=
pi*I
1 + ------
log(5)
$$1 + \frac{i \pi}{\log{\left(5 \right)}}$$
product
pi*I
1 + ------
log(5)
$$1 + \frac{i \pi}{\log{\left(5 \right)}}$$
=
pi*I
1 + ------
log(5)
$$1 + \frac{i \pi}{\log{\left(5 \right)}}$$
1 + pi*i/log(5)
Rapid solution
[src]
pi*I
x1 = 1 + ------
log(5)
$$x_{1} = 1 + \frac{i \pi}{\log{\left(5 \right)}}$$
x1 = 1 + i*pi/log(5)
The graph