Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x/4+13=x+1
-
Equation 4(x-8)=-5
-
Equation 3x-2=0
-
Equation x*8=25+15
- Express {x} in terms of y where:
- 4*x+8*y=7
- -14*x+5*y=3
- 13*x-18*y=-17
- 4*x+18*y=-7
-
Identical expressions
- eight / four ^x- six * two ^x+ one = zero
- 8 divide by 4 to the power of x minus 6 multiply by 2 to the power of x plus 1 equally 0
- eight divide by four to the power of x minus six multiply by two to the power of x plus one equally zero
- 8/4x-6*2x+1=0
- 8/4^x-62^x+1=0
- 8/4x-62x+1=0
- 8/4^x-6*2^x+1=O
- 8 divide by 4^x-6*2^x+1=0
-
Similar expressions
- 8/4^x-6*2^x-1=0
- 8/4^x+6*2^x+1=0
8/4^x-6*2^x+1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation:
$$- 6 \cdot 2^{x} + 2^{x} + 1 = 0$$
or
$$\left(- 6 \cdot 2^{x} + 2^{x} + 1\right) + 0 = 0$$
or
$$- 5 \cdot 2^{x} = -1$$
or
$$2^{x} = \frac{1}{5}$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
we get
$$v - \frac{1}{5} = 0$$
or
$$v - \frac{1}{5} = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = \frac{1}{5}$$
We get the answer: v = 1/5
do backward replacement
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(\frac{1}{5} \right)}}{\log{\left(2 \right)}} = - \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
$$- 6 \cdot 2^{x} + 2^{x} + 1 = 0$$
or
$$\left(- 6 \cdot 2^{x} + 2^{x} + 1\right) + 0 = 0$$
or
$$- 5 \cdot 2^{x} = -1$$
or
$$2^{x} = \frac{1}{5}$$
- this is the simplest exponential equation
Do replacement
$$v = 2^{x}$$
we get
$$v - \frac{1}{5} = 0$$
or
$$v - \frac{1}{5} = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = \frac{1}{5}$$
We get the answer: v = 1/5
do backward replacement
$$2^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(2 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(\frac{1}{5} \right)}}{\log{\left(2 \right)}} = - \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
Rapid solution
[src]
-log(5)
x_1 = --------
log(2)
$$x_{1} = - \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
Sum and product of roots
[src]
sum
-log(5) -------- log(2)
$$\left(- \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}\right)$$
=
-log(5) -------- log(2)
$$- \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
product
-log(5) -------- log(2)
$$\left(- \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}\right)$$
=
-log(5) -------- log(2)
$$- \frac{\log{\left(5 \right)}}{\log{\left(2 \right)}}$$
The graph