Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 4x+2(1-3x)=13
-
Equation x^2-10x+25=0
- Equation x-y=0
-
Equation 3-x=1+x
- Express {x} in terms of y where:
- -2*x-4*y=11
- 14*x-3*y=-9
- 6*x-19*y=-18
- 10*x-5*y=3
- Derivative of:
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3^x
- Integral of d{x}:
-
3^x
- Graphing y =:
- 3^x
-
Identical expressions
- three ^x= two hundred and forty-three
- 3 to the power of x equally 243
- three to the power of x equally two hundred and forty minus three
- 3x=243
-
Similar expressions
- 9^x+3*3^x-18=0
3^x=243 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$3^{x} = 243$$
or
$$3^{x} - 243 = 0$$
or
$$3^{x} = 243$$
or
$$3^{x} = 243$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 243 = 0$$
or
$$v - 243 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 243$$
We get the answer: v = 243
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(243 \right)}}{\log{\left(3 \right)}} = 5$$
$$3^{x} = 243$$
or
$$3^{x} - 243 = 0$$
or
$$3^{x} = 243$$
or
$$3^{x} = 243$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 243 = 0$$
or
$$v - 243 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 243$$
We get the answer: v = 243
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(243 \right)}}{\log{\left(3 \right)}} = 5$$
The graph