Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3^x=27
-
Equation x^2=12
-
Equation 12-x^2=11
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Equation -sin(x)=0
- Express {x} in terms of y where:
- -4*x+19*y=-13
- -5*x-6*y=-1
- -7*x+15*y=18
- -11*x+10*y=-3
- Derivative of:
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3^x
- Integral of d{x}:
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3^x
- Graphing y =:
- 3^x
- Sum of series:
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27
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Identical expressions
- three ^x= twenty-seven
- 3 to the power of x equally 27
- three to the power of x equally twenty minus seven
- 3x=27
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Similar expressions
- 5(x-3)=14-2(7-2x)
- 2^(3*(x-1/x))*3^x=3
3^x=27 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$3^{x} = 27$$
or
$$3^{x} - 27 = 0$$
or
$$3^{x} = 27$$
or
$$3^{x} = 27$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 27 = 0$$
or
$$v - 27 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 27$$
We get the answer: v = 27
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(27 \right)}}{\log{\left(3 \right)}} = 3$$
$$3^{x} = 27$$
or
$$3^{x} - 27 = 0$$
or
$$3^{x} = 27$$
or
$$3^{x} = 27$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 27 = 0$$
or
$$v - 27 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 27$$
We get the answer: v = 27
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(27 \right)}}{\log{\left(3 \right)}} = 3$$
The graph