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  • Inequation:
  • 3*lg^2(x-8)/(lg^2(x-4))>=2
  • logx(4x-3)>=2
  • -4x^2+6*x<=0
  • 6^|x-3|*log(3)6x-x^2-6>=1

  • Identical expressions

  • three *lg^ two (x- eight)/(lg^ two (x- four))>= two
  • 3 multiply by lg squared (x minus 8) divide by (lg squared (x minus 4)) greater than or equal to 2
  • three multiply by lg to the power of two (x minus eight) divide by (lg to the power of two (x minus four)) greater than or equal to two
  • 3*lg2(x-8)/(lg2(x-4))>=2
  • 3*lg2x-8/lg2x-4>=2
  • 3*lg²(x-8)/(lg²(x-4))>=2
  • 3*lg to the power of 2(x-8)/(lg to the power of 2(x-4))>=2
  • 3lg^2(x-8)/(lg^2(x-4))>=2
  • 3lg2(x-8)/(lg2(x-4))>=2
  • 3lg2x-8/lg2x-4>=2
  • 3lg^2x-8/lg^2x-4>=2
  • 3*lg^2(x-8) divide by (lg^2(x-4))>=2

  • Similar expressions

  • 3*lg^2(x-8)/(lg^2(x+4))>=2
  • 3*lg^2(x+8)/(lg^2(x-4))>=2
Solving inequalities/ 3*lg^2(x-8)/(lg^2(x-4))>=2

3*lg^2(x-8)/(lg^2(x-4))>=2 inequation

A inequation with variable

The solution

You have entered [src] 
     2            
3*log (x - 8)     
------------- >= 2
    2             
 log (x - 4)
$$\frac{3 \log{\left(x - 8 \right)}^{2}}{\log{\left(x - 4 \right)}^{2}} \geq 2$$ 
3*log(x - 1*8)^2/(log(x - 1*4)^2) >= 2
Detail solution
Given the inequality:
$$\frac{3 \log{\left(x - 8 \right)}^{2}}{\log{\left(x - 4 \right)}^{2}} \geq 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{3 \log{\left(x - 8 \right)}^{2}}{\log{\left(x - 4 \right)}^{2}} = 2$$
Solve:
$$x_{1} = 15.1773834231572$$
$$x_{1} = 15.1773834231572$$
This roots
$$x_{1} = 15.1773834231572$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 15.1773834231572$$
=
$$15.0773834231572$$
substitute to the expression
$$\frac{3 \log{\left(x - 8 \right)}^{2}}{\log{\left(x - 4 \right)}^{2}} \geq 2$$
$$\frac{3 \log{\left(\left(-1\right) 8 + 15.0773834231572 \right)}^{2}}{\log{\left(\left(-1\right) 4 + 15.0773834231572 \right)}^{2}} \geq 2$$
1.98638937528934 >= 2

but
1.98638937528934 < 2

Then
$$x \leq 15.1773834231572$$
no execute
the solution of our inequality is:
$$x \geq 15.1773834231572$$
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