Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2-12x+36=0
-
Equation 8x^2=0
- Equation 1,11^(x)=2
- Equation (x+5)^4-(13*x^2)*(x+5)^2+36x^4=0
- Express {x} in terms of y where:
- -16*x-14*y=-9
- 14*x-16*y=-3
- 17*x-20*y=6
- 10*x-19*y=3
-
Identical expressions
- one , eleven ^(x)= two
- 1,11 to the power of (x) equally 2
- one , eleven to the power of (x) equally two
- 1,11(x)=2
- 1,11x=2
- 1,11^x=2
1,11^(x)=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$\left(\frac{111}{100}\right)^{x} = 2$$
or
$$\left(\frac{111}{100}\right)^{x} - 2 = 0$$
or
$$\left(\frac{111}{100}\right)^{x} = 2$$
or
$$\left(\frac{111}{100}\right)^{x} = 2$$
- this is the simplest exponential equation
Do replacement
$$v = \left(\frac{111}{100}\right)^{x}$$
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
$$\left(\frac{111}{100}\right)^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(\frac{111}{100} \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(2 \right)}}{\log{\left(\frac{111}{100} \right)}} = \log{\left(2^{\frac{1}{\log{\left(\frac{111}{100} \right)}}} \right)}$$
$$\left(\frac{111}{100}\right)^{x} = 2$$
or
$$\left(\frac{111}{100}\right)^{x} - 2 = 0$$
or
$$\left(\frac{111}{100}\right)^{x} = 2$$
or
$$\left(\frac{111}{100}\right)^{x} = 2$$
- this is the simplest exponential equation
Do replacement
$$v = \left(\frac{111}{100}\right)^{x}$$
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
$$\left(\frac{111}{100}\right)^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(\frac{111}{100} \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(2 \right)}}{\log{\left(\frac{111}{100} \right)}} = \log{\left(2^{\frac{1}{\log{\left(\frac{111}{100} \right)}}} \right)}$$
Rapid solution
[src]
/ 1 \
| --------|
| /111\|
| log|---||
| \100/|
x1 = log\2 /
$$x_{1} = \log{\left(2^{\frac{1}{\log{\left(\frac{111}{100} \right)}}} \right)}$$
x1 = log(2^(1/log(111/100)))
Sum and product of roots
[src]
sum
/ 1 \ | --------| | /111\| | log|---|| | \100/| log\2 /
$$\log{\left(2^{\frac{1}{\log{\left(\frac{111}{100} \right)}}} \right)}$$
=
/ 1 \ | --------| | /111\| | log|---|| | \100/| log\2 /
$$\log{\left(2^{\frac{1}{\log{\left(\frac{111}{100} \right)}}} \right)}$$
product
/ 1 \ | --------| | /111\| | log|---|| | \100/| log\2 /
$$\log{\left(2^{\frac{1}{\log{\left(\frac{111}{100} \right)}}} \right)}$$
=
/ 1 \ | --------| | /111\| | log|---|| | \100/| log\2 /
$$\log{\left(2^{\frac{1}{\log{\left(\frac{111}{100} \right)}}} \right)}$$
log(2^(1/log(111/100)))