Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
-
x^2+11x+18>0
- x^2-81〈0
- log8(x-9)<1/3
- 1-sin(x)(log3(x))>=log3(x)-sin(x)
- Sum of series:
-
1/3
- Derivative of:
-
1/3
- Limit of the function:
- 1/3
-
Identical expressions
- log8(x- nine)< one / three
- logarithm of 8(x minus 9) less than 1 divide by 3
- logarithm of 8(x minus nine) less than one divide by three
- log8x-9<1/3
- log8(x-9)<1 divide by 3
-
Similar expressions
- log8(x+9)<1/3
- (9^(x+1)-22*3^(x+1)-135)*1/(3^(x+1)-1)>=0
log8(x-9)<1/3 inequation
The solution
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log(x - 9) ---------- < 1/3 log(8)
$$\frac{\log{\left(x - 9 \right)}}{\log{\left(8 \right)}} < \frac{1}{3}$$
log(x - 9)/log(8) < 1/3
Detail solution
Given the inequality:
$$\frac{\log{\left(x - 9 \right)}}{\log{\left(8 \right)}} < \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(x - 9 \right)}}{\log{\left(8 \right)}} = \frac{1}{3}$$
Solve:
Given the equation
$$\frac{\log{\left(x - 9 \right)}}{\log{\left(8 \right)}} = \frac{1}{3}$$
$$\frac{\log{\left(x - 9 \right)}}{\log{\left(8 \right)}} = \frac{1}{3}$$
Let's divide both parts of the equation by the multiplier of log =1/log(8)
$$\log{\left(x - 9 \right)} = \frac{\log{\left(8 \right)}}{3}$$
This equation is of the form:
By definition log
then
$$x - 9 = e^{\frac{1}{3 \frac{1}{\log{\left(8 \right)}}}}$$
simplify
$$x - 9 = 2$$
$$x = 11$$
$$x_{1} = 11$$
$$x_{1} = 11$$
This roots
$$x_{1} = 11$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 11$$
=
$$\frac{109}{10}$$
substitute to the expression
$$\frac{\log{\left(x - 9 \right)}}{\log{\left(8 \right)}} < \frac{1}{3}$$
$$\frac{\log{\left(-9 + \frac{109}{10} \right)}}{\log{\left(8 \right)}} < \frac{1}{3}$$
the solution of our inequality is:
$$x < 11$$
$$\frac{\log{\left(x - 9 \right)}}{\log{\left(8 \right)}} < \frac{1}{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(x - 9 \right)}}{\log{\left(8 \right)}} = \frac{1}{3}$$
Solve:
Given the equation
$$\frac{\log{\left(x - 9 \right)}}{\log{\left(8 \right)}} = \frac{1}{3}$$
$$\frac{\log{\left(x - 9 \right)}}{\log{\left(8 \right)}} = \frac{1}{3}$$
Let's divide both parts of the equation by the multiplier of log =1/log(8)
$$\log{\left(x - 9 \right)} = \frac{\log{\left(8 \right)}}{3}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$x - 9 = e^{\frac{1}{3 \frac{1}{\log{\left(8 \right)}}}}$$
simplify
$$x - 9 = 2$$
$$x = 11$$
$$x_{1} = 11$$
$$x_{1} = 11$$
This roots
$$x_{1} = 11$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 11$$
=
$$\frac{109}{10}$$
substitute to the expression
$$\frac{\log{\left(x - 9 \right)}}{\log{\left(8 \right)}} < \frac{1}{3}$$
$$\frac{\log{\left(-9 + \frac{109}{10} \right)}}{\log{\left(8 \right)}} < \frac{1}{3}$$
/19\ log|--| \10/ < 1/3 ------- log(8)
the solution of our inequality is:
$$x < 11$$
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Solving inequality on a graph