Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+4*x+4=0
-
Equation (x^2-4)^2+(x^2-3x-10)^2=0
-
Equation -x/3+x+7=3
-
Equation -20*(x-13)=-220
- Express {x} in terms of y where:
- -14*x+4*y=-16
- -13*x-10*y=5
- 9*x-1*y=17
- -12*x-8*y=13
- Derivative of:
-
3^x
- Integral of d{x}:
-
3^x
- Graphing y =:
- 3^x
-
Identical expressions
- three ^x= two
- 3 to the power of x equally 2
- three to the power of x equally two
- 3x=2
-
Similar expressions
- 2^(3*(x-1/x))*3^x=3
- 3^x=243
- -3^(x+2)+9^x+14=0
3^x=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$3^{x} = 2$$
or
$$3^{x} - 2 = 0$$
or
$$3^{x} = 2$$
or
$$3^{x} = 2$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 2 = 0$$
or
$$v - 2 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 2$$
We get the answer: v = 2
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(2 \right)}}{\log{\left(3 \right)}} = \frac{\log{\left(2 \right)}}{\log{\left(3 \right)}}$$
$$3^{x} = 2$$
or
$$3^{x} - 2 = 0$$
or
$$3^{x} = 2$$
or
$$3^{x} = 2$$
- this is the simplest exponential equation
Do replacement
$$v = 3^{x}$$
we get
$$v - 2 = 0$$
or
$$v - 2 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 2$$
We get the answer: v = 2
do backward replacement
$$3^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(3 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(2 \right)}}{\log{\left(3 \right)}} = \frac{\log{\left(2 \right)}}{\log{\left(3 \right)}}$$
Sum and product of roots
[src]
sum
log(2) ------ log(3)
$$\frac{\log{\left(2 \right)}}{\log{\left(3 \right)}}$$
=
log(2) ------ log(3)
$$\frac{\log{\left(2 \right)}}{\log{\left(3 \right)}}$$
product
log(2) ------ log(3)
$$\frac{\log{\left(2 \right)}}{\log{\left(3 \right)}}$$
=
log(2) ------ log(3)
$$\frac{\log{\left(2 \right)}}{\log{\left(3 \right)}}$$
log(2)/log(3)
Rapid solution
[src]
log(2)
x1 = ------
log(3)
$$x_{1} = \frac{\log{\left(2 \right)}}{\log{\left(3 \right)}}$$
x1 = log(2)/log(3)
The graph