Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- 22x-9≤1
- 12*log(2*u)-20>=log(2)/((2*u))
- (x-4)*(x-9)<=0
- 29*9^x-26*3^x-1>0
- Derivative of:
-
7^x
- Graphing y =:
- 7^x
- Integral of d{x}:
-
7^x
-
Identical expressions
- seven ^x<= nine
- 7 to the power of x less than or equal to 9
- seven to the power of x less than or equal to nine
- 7x<=9
7^x<=9 inequation
The solution
Detail solution
Given the inequality:
$$7^{x} \leq 9$$
To solve this inequality, we must first solve the corresponding equation:
$$7^{x} = 9$$
Solve:
Given the equation:
$$7^{x} = 9$$
or
$$7^{x} - 9 = 0$$
or
$$7^{x} = 9$$
or
$$7^{x} = 9$$
- this is the simplest exponential equation
Do replacement
$$v = 7^{x}$$
we get
$$v - 9 = 0$$
or
$$v - 9 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 9$$
do backward replacement
$$7^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(7 \right)}}$$
$$x_{1} = 9$$
$$x_{1} = 9$$
This roots
$$x_{1} = 9$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 9$$
=
$$\frac{89}{10}$$
substitute to the expression
$$7^{x} \leq 9$$
$$7^{\frac{89}{10}} \leq 9$$
but
Then
$$x \leq 9$$
no execute
the solution of our inequality is:
$$x \geq 9$$
$$7^{x} \leq 9$$
To solve this inequality, we must first solve the corresponding equation:
$$7^{x} = 9$$
Solve:
Given the equation:
$$7^{x} = 9$$
or
$$7^{x} - 9 = 0$$
or
$$7^{x} = 9$$
or
$$7^{x} = 9$$
- this is the simplest exponential equation
Do replacement
$$v = 7^{x}$$
we get
$$v - 9 = 0$$
or
$$v - 9 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 9$$
do backward replacement
$$7^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(7 \right)}}$$
$$x_{1} = 9$$
$$x_{1} = 9$$
This roots
$$x_{1} = 9$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 9$$
=
$$\frac{89}{10}$$
substitute to the expression
$$7^{x} \leq 9$$
$$7^{\frac{89}{10}} \leq 9$$
9/10
5764801*7 <= 9
but
9/10
5764801*7 >= 9
Then
$$x \leq 9$$
no execute
the solution of our inequality is:
$$x \geq 9$$
_____
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x1
Solving inequality on a graph
Rapid solution 2
[src]
log(9)
(-oo, ------]
log(7)
$$x\ in\ \left(-\infty, \frac{\log{\left(9 \right)}}{\log{\left(7 \right)}}\right]$$
x in Interval(-oo, log(9)/log(7))
Rapid solution
[src]
log(9)
x <= ------
log(7)
$$x \leq \frac{\log{\left(9 \right)}}{\log{\left(7 \right)}}$$
x <= log(9)/log(7)