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
- Integral of d{x}:
-
2^x
- Derivative of:
-
2^x
- Graphing y =:
- 2^x
-
Identical expressions
- two ^x= three
- 2 to the power of x equally 3
- two to the power of x equally three
- 2x=3
2^x=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$2^{x} = 3$$
or
$$2^{x} - 3 = 0$$
or
$$2^{x} = 3$$
or
$$2^{x} = 3$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
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
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(3 \right)}}{\log{\left(2 \right)}} = \frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
$$2^{x} = 3$$
or
$$2^{x} - 3 = 0$$
or
$$2^{x} = 3$$
or
$$2^{x} = 3$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
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
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(3 \right)}}{\log{\left(2 \right)}} = \frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
Sum and product of roots
[src]
sum
log(3) ------ log(2)
$$\frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
=
log(3) ------ log(2)
$$\frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
product
log(3) ------ log(2)
$$\frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
=
log(3) ------ log(2)
$$\frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
log(3)/log(2)
Rapid solution
[src]
log(3)
x1 = ------
log(2)
$$x_{1} = \frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
x1 = log(3)/log(2)
The graph