Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation a*x=b
-
Equation 2-3(2+3x)=14
-
Equation x^2-x+8=0
-
Equation 2^x=7
- Express {x} in terms of y where:
- 8*x-4*y=10
- -17*x-5*y=-20
- 2*x+19*y=-7
- -4*x+7*y=-16
- Derivative of:
-
2^x
- Integral of d{x}:
-
2^x
- Graphing y =:
- 2^x
-
Identical expressions
- two ^x= seven
- 2 to the power of x equally 7
- two to the power of x equally seven
- 2x=7
2^x=7 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$2^{x} = 7$$
or
$$2^{x} - 7 = 0$$
or
$$2^{x} = 7$$
or
$$2^{x} = 7$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
we get
$$v - 7 = 0$$
or
$$v - 7 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 7$$
We get the answer: v = 7
do backward replacement
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(7 \right)}}{\log{\left(2 \right)}} = \frac{\log{\left(7 \right)}}{\log{\left(2 \right)}}$$
$$2^{x} = 7$$
or
$$2^{x} - 7 = 0$$
or
$$2^{x} = 7$$
or
$$2^{x} = 7$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
we get
$$v - 7 = 0$$
or
$$v - 7 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 7$$
We get the answer: v = 7
do backward replacement
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(7 \right)}}{\log{\left(2 \right)}} = \frac{\log{\left(7 \right)}}{\log{\left(2 \right)}}$$
Sum and product of roots
[src]
sum
log(7) ------ log(2)
$$\frac{\log{\left(7 \right)}}{\log{\left(2 \right)}}$$
=
log(7) ------ log(2)
$$\frac{\log{\left(7 \right)}}{\log{\left(2 \right)}}$$
product
log(7) ------ log(2)
$$\frac{\log{\left(7 \right)}}{\log{\left(2 \right)}}$$
=
log(7) ------ log(2)
$$\frac{\log{\left(7 \right)}}{\log{\left(2 \right)}}$$
log(7)/log(2)
Rapid solution
[src]
log(7)
x1 = ------
log(2)
$$x_{1} = \frac{\log{\left(7 \right)}}{\log{\left(2 \right)}}$$
x1 = log(7)/log(2)
The graph