Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+3x+2=0
- Equation x+y=5
-
Equation sin(x)=3
-
Equation x^2-11*x+30=0
- Express {x} in terms of y where:
- 6*x+17*y=-11
- -13*x+7*y=-15
- -14*x-8*y=20
- 9*x+14*y=-10
- Derivative of:
-
2^x
- Integral of d{x}:
-
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
-
Similar expressions
- 4(2x-16)^2-19(2x-16)+12=0
- 2^x=2*x+8
- 8/4^x-6*2^x+1=0
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