Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 81*x^3+18*x^2+x=0
-
Equation 6=8-5(7x-1)
-
Equation 3x=28-x
-
Equation 3x=2
- Express {x} in terms of y where:
- -13*x-7*y=16
- -16*x+10*y=-11
- -2*x-15*y=-1
- -14*x+5*y=-1
- Integral of d{x}:
-
2^x
- Derivative of:
-
2^x
- Graphing y =:
- 2^x
-
Identical expressions
- two ^x= sixteen ^ two
- 2 to the power of x equally 16 squared
- two to the power of x equally sixteen to the power of two
- 2x=162
- 2^x=16²
- 2 to the power of x=16 to the power of 2
2^x=16^2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$2^{x} = 16^{2}$$
or
$$2^{x} - 16^{2} = 0$$
or
$$2^{x} = 256$$
or
$$2^{x} = 256$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
we get
$$v - 256 = 0$$
or
$$v - 256 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 256$$
We get the answer: v = 256
do backward replacement
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(256 \right)}}{\log{\left(2 \right)}} = 8$$
$$2^{x} = 16^{2}$$
or
$$2^{x} - 16^{2} = 0$$
or
$$2^{x} = 256$$
or
$$2^{x} = 256$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
we get
$$v - 256 = 0$$
or
$$v - 256 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 256$$
We get the answer: v = 256
do backward replacement
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(256 \right)}}{\log{\left(2 \right)}} = 8$$
Sum and product of roots
[src]
sum
8
$$\left(8\right)$$
=
8
$$8$$
product
8
$$\left(8\right)$$
=
8
$$8$$
The graph