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-3)√x^2-√1<0
- (x^2-7|x|+10)/(x^2-6x+9)>=0
- 5x^2-2x^4+7>0
- log(x)/log(3/5)>1/2
- Sum of series:
-
1/2
- Derivative of:
-
1/2
- Integral of d{x}:
-
1/2
-
Identical expressions
- log(x)/log(three / five)> one / two
- logarithm of (x) divide by logarithm of (3 divide by 5) greater than 1 divide by 2
- logarithm of (x) divide by logarithm of (three divide by five) greater than one divide by two
- logx/log3/5>1/2
- log(x) divide by log(3 divide by 5)>1 divide by 2
log(x)/log(3/5)>1/2 inequation
The solution
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[src]
log(x) -------- > 1/2 log(3/5)
$$\frac{\log{\left(x \right)}}{\log{\left(\frac{3}{5} \right)}} > \frac{1}{2}$$
log(x)/log(3/5) > 1/2
Detail solution
Given the inequality:
$$\frac{\log{\left(x \right)}}{\log{\left(\frac{3}{5} \right)}} > \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(x \right)}}{\log{\left(\frac{3}{5} \right)}} = \frac{1}{2}$$
Solve:
Given the equation
$$\frac{\log{\left(x \right)}}{\log{\left(\frac{3}{5} \right)}} = \frac{1}{2}$$
$$\frac{\log{\left(x \right)}}{\log{\left(\frac{3}{5} \right)}} = \frac{1}{2}$$
Let's divide both parts of the equation by the multiplier of log =1/log(3/5)
$$\log{\left(x \right)} = \frac{\log{\left(\frac{3}{5} \right)}}{2}$$
This equation is of the form:
By definition log
then
$$x = e^{\frac{1}{2 \frac{1}{\log{\left(\frac{3}{5} \right)}}}}$$
simplify
$$x = \frac{\sqrt{15}}{5}$$
$$x_{1} = \frac{\sqrt{15}}{5}$$
$$x_{1} = \frac{\sqrt{15}}{5}$$
This roots
$$x_{1} = \frac{\sqrt{15}}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{\sqrt{15}}{5}$$
=
$$- \frac{1}{10} + \frac{\sqrt{15}}{5}$$
substitute to the expression
$$\frac{\log{\left(x \right)}}{\log{\left(\frac{3}{5} \right)}} > \frac{1}{2}$$
$$\frac{\log{\left(- \frac{1}{10} + \frac{\sqrt{15}}{5} \right)}}{\log{\left(\frac{3}{5} \right)}} > \frac{1}{2}$$
the solution of our inequality is:
$$x < \frac{\sqrt{15}}{5}$$
$$\frac{\log{\left(x \right)}}{\log{\left(\frac{3}{5} \right)}} > \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(x \right)}}{\log{\left(\frac{3}{5} \right)}} = \frac{1}{2}$$
Solve:
Given the equation
$$\frac{\log{\left(x \right)}}{\log{\left(\frac{3}{5} \right)}} = \frac{1}{2}$$
$$\frac{\log{\left(x \right)}}{\log{\left(\frac{3}{5} \right)}} = \frac{1}{2}$$
Let's divide both parts of the equation by the multiplier of log =1/log(3/5)
$$\log{\left(x \right)} = \frac{\log{\left(\frac{3}{5} \right)}}{2}$$
This equation is of the form:
log(v)=p
By definition log
v=e^p
then
$$x = e^{\frac{1}{2 \frac{1}{\log{\left(\frac{3}{5} \right)}}}}$$
simplify
$$x = \frac{\sqrt{15}}{5}$$
$$x_{1} = \frac{\sqrt{15}}{5}$$
$$x_{1} = \frac{\sqrt{15}}{5}$$
This roots
$$x_{1} = \frac{\sqrt{15}}{5}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{\sqrt{15}}{5}$$
=
$$- \frac{1}{10} + \frac{\sqrt{15}}{5}$$
substitute to the expression
$$\frac{\log{\left(x \right)}}{\log{\left(\frac{3}{5} \right)}} > \frac{1}{2}$$
$$\frac{\log{\left(- \frac{1}{10} + \frac{\sqrt{15}}{5} \right)}}{\log{\left(\frac{3}{5} \right)}} > \frac{1}{2}$$
/ ____\
| 1 \/ 15 |
log|- -- + ------|
\ 10 5 / > 1/2
------------------
log(3/5)
the solution of our inequality is:
$$x < \frac{\sqrt{15}}{5}$$
_____
\
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x1
Solving inequality on a graph