Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -x=25
-
Equation x^3=5
-
Equation 2x=4
-
Equation x^2=x+72
- Express {x} in terms of y where:
- 11*x+3*y=-16
- -2*x+13*y=-6
- 20*x-3*y=3
- 18*x-7*y=-4
- Derivative of:
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2^x
-
10
- Integral of d{x}:
-
2^x
-
10
- Graphing y =:
- 2^x
- Sum of series:
-
10
-
Identical expressions
- two ^x= ten
- 2 to the power of x equally 10
- two to the power of x equally ten
- 2x=10
2^x=10 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$2^{x} = 10$$
or
$$2^{x} - 10 = 0$$
or
$$2^{x} = 10$$
or
$$2^{x} = 10$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
we get
$$v - 10 = 0$$
or
$$v - 10 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 10$$
We get the answer: v = 10
do backward replacement
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(10 \right)}}{\log{\left(2 \right)}} = 1 + \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
$$2^{x} = 10$$
or
$$2^{x} - 10 = 0$$
or
$$2^{x} = 10$$
or
$$2^{x} = 10$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
we get
$$v - 10 = 0$$
or
$$v - 10 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 10$$
We get the answer: v = 10
do backward replacement
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(10 \right)}}{\log{\left(2 \right)}} = 1 + \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
Sum and product of roots
[src]
sum
log(5)
1 + ------
log(2)
$$1 + \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
=
log(5)
1 + ------
log(2)
$$1 + \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
product
log(5)
1 + ------
log(2)
$$1 + \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
=
log(10) ------- log(2)
$$\frac{\log{\left(10 \right)}}{\log{\left(2 \right)}}$$
log(10)/log(2)
Rapid solution
[src]
log(5)
x1 = 1 + ------
log(2)
$$x_{1} = 1 + \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
x1 = 1 + log(5)/log(2)
The graph