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How to use it?
- Inequation:
-
(3^(2x-1)+3^(2x-2)-3^(2x-4))<=315
- lg(6)+x*lg(5)>=x+lg(2^x+1)
- sin(x)>sqrt-2/2
- (0,1)^(x^2-4x-15/x+1)>=0,001
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Identical expressions
- (three ^(two x- one)+ three ^(2x-2)- three ^(2x- four))<= three hundred and fifteen
- (3 to the power of (2x minus 1) plus 3 to the power of (2x minus 2) minus 3 to the power of (2x minus 4)) less than or equal to 315
- (three to the power of (two x minus one) plus three to the power of (2x minus 2) minus three to the power of (2x minus four)) less than or equal to three hundred and fifteen
- (3(2x-1)+3(2x-2)-3(2x-4))<=315
- 32x-1+32x-2-32x-4<=315
- 3^2x-1+3^2x-2-3^2x-4<=315
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Similar expressions
- (3^(2x-1)+3^(2x-2)-3^(2x+4))<=315
- (3^(2x+1)+3^(2x-2)-3^(2x-4))<=315
- (3^(2x-1)+3^(2x+2)-3^(2x-4))<=315
- (3^(2x-1)-3^(2x-2)-3^(2x-4))<=315
- (3^(2x-1)+3^(2x-2)+3^(2x-4))<=315
(3^(2x-1)+3^(2x-2)-3^(2x-4))<=315 inequation
The solution
You have entered
[src]
2*x - 1 2*x - 2 2*x - 4 3 + 3 - 3 <= 315
$$3^{2 x - 1} + 3^{2 x - 2} - 3^{2 x - 4} \leq 315$$
3^(2*x - 1*1) + 3^(2*x - 1*2) - 3^(2*x - 1*4) <= 315
Detail solution
Given the inequality:
$$3^{2 x - 1} + 3^{2 x - 2} - 3^{2 x - 4} \leq 315$$
To solve this inequality, we must first solve the corresponding equation:
$$3^{2 x - 1} + 3^{2 x - 2} - 3^{2 x - 4} = 315$$
Solve:
$$x_{1} = 3$$
$$x_{2} = \frac{\log{\left(27 \right)} + i \pi}{\log{\left(3 \right)}}$$
Exclude the complex solutions:
$$x_{1} = 3$$
This roots
$$x_{1} = 3$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 3$$
=
$$\frac{29}{10}$$
substitute to the expression
$$3^{2 x - 1} + 3^{2 x - 2} - 3^{2 x - 4} \leq 315$$
$$- 3^{\left(-1\right) 4 + 2 \cdot \frac{29}{10}} + 3^{\left(-1\right) 2 + 2 \cdot \frac{29}{10}} + 3^{\left(-1\right) 1 + 2 \cdot \frac{29}{10}} \leq 315$$
the solution of our inequality is:
$$x \leq 3$$
$$3^{2 x - 1} + 3^{2 x - 2} - 3^{2 x - 4} \leq 315$$
To solve this inequality, we must first solve the corresponding equation:
$$3^{2 x - 1} + 3^{2 x - 2} - 3^{2 x - 4} = 315$$
Solve:
$$x_{1} = 3$$
$$x_{2} = \frac{\log{\left(27 \right)} + i \pi}{\log{\left(3 \right)}}$$
Exclude the complex solutions:
$$x_{1} = 3$$
This roots
$$x_{1} = 3$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 3$$
=
$$\frac{29}{10}$$
substitute to the expression
$$3^{2 x - 1} + 3^{2 x - 2} - 3^{2 x - 4} \leq 315$$
$$- 3^{\left(-1\right) 4 + 2 \cdot \frac{29}{10}} + 3^{\left(-1\right) 2 + 2 \cdot \frac{29}{10}} + 3^{\left(-1\right) 1 + 2 \cdot \frac{29}{10}} \leq 315$$
4/5
105*3 <= 315
the solution of our inequality is:
$$x \leq 3$$
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x_1
Solving inequality on a graph
Rapid solution 2
[src]
log(27)
(-oo, -------]
log(3)
$$x\ in\ \left(-\infty, \frac{\log{\left(27 \right)}}{\log{\left(3 \right)}}\right]$$
x in Interval(-oo, log(27)/log(3))
Rapid solution
[src]
log(27)
x <= -------
log(3)
$$x \leq \frac{\log{\left(27 \right)}}{\log{\left(3 \right)}}$$
x <= log(27)/log(3)
The graph