Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2x-3(x+3)=-5
-
Equation 2x-3=4
-
Equation 6=8-5(7x-1)
-
Equation 5(x-2)^2=-6x-44
- Express {x} in terms of y where:
- -14*x+10*y=19
- 5*x-14*y=-15
- -7*x+15*y=-11
- -18*x-14*y=12
- Graphing y =:
- (1/10)^x
- Limit of the function:
-
(1/10)^x
- Sum of series:
-
100
- Canonical form:
- 100
- Integral of d{x}:
-
100
-
Identical expressions
- (one / ten)^x= one hundred
- (1 divide by 10) to the power of x equally 100
- (one divide by ten) to the power of x equally one hundred
- (1/10)x=100
- 1/10x=100
- 1/10^x=100
- (1 divide by 10)^x=100
(1/10)^x=100 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$\left(\frac{1}{10}\right)^{x} = 100$$
or
$$-100 + \left(\frac{1}{10}\right)^{x} = 0$$
or
$$\left(\frac{1}{10}\right)^{x} = 100$$
or
$$\left(\frac{1}{10}\right)^{x} = 100$$
- this is the simplest exponential equation
Do replacement
$$v = \left(\frac{1}{10}\right)^{x}$$
we get
$$v - 100 = 0$$
or
$$v - 100 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 100$$
We get the answer: v = 100
do backward replacement
$$\left(\frac{1}{10}\right)^{x} = v$$
or
$$x = - \frac{\log{\left(v \right)}}{\log{\left(10 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(100 \right)}}{\log{\left(\frac{1}{10} \right)}} = -2$$
$$\left(\frac{1}{10}\right)^{x} = 100$$
or
$$-100 + \left(\frac{1}{10}\right)^{x} = 0$$
or
$$\left(\frac{1}{10}\right)^{x} = 100$$
or
$$\left(\frac{1}{10}\right)^{x} = 100$$
- this is the simplest exponential equation
Do replacement
$$v = \left(\frac{1}{10}\right)^{x}$$
we get
$$v - 100 = 0$$
or
$$v - 100 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 100$$
We get the answer: v = 100
do backward replacement
$$\left(\frac{1}{10}\right)^{x} = v$$
or
$$x = - \frac{\log{\left(v \right)}}{\log{\left(10 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(100 \right)}}{\log{\left(\frac{1}{10} \right)}} = -2$$
Sum and product of roots
[src]
sum
0 - 2
$$-2 + 0$$
=
-2
$$-2$$
product
1*-2
$$1 \left(-2\right)$$
=
-2
$$-2$$
-2
The graph