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  • Inequation:
  • 25^((1/x-1))-4*5^((1/x)-1)-5=>0
  • (1/4)^2>=8
  • x+3.3<=0
  • (3x-5)^0,5<5

  • Identical expressions

  • lg(three *x+ two *sqrt(x)- two)* one /(lg(five *x+ three *sqrt(x)- three)^ three)>=(log(ten)/log(twenty-seven))/(log(ten)/log(three)(ten))
  • lg(3 multiply by x plus 2 multiply by square root of (x) minus 2) multiply by 1 divide by (lg(5 multiply by x plus 3 multiply by square root of (x) minus 3) cubed ) greater than or equal to ( logarithm of (10) divide by logarithm of (27)) divide by ( logarithm of (10) divide by logarithm of (3)(10))
  • lg(three multiply by x plus two multiply by square root of (x) minus two) multiply by one divide by (lg(five multiply by x plus three multiply by square root of (x) minus three) to the power of three) greater than or equal to ( logarithm of (ten) divide by logarithm of (twenty minus seven)) divide by ( logarithm of (ten) divide by logarithm of (three)(ten))
  • lg(3*x+2*√(x)-2)*1/(lg(5*x+3*√(x)-3)^3)>=(log(10)/log(27))/(log(10)/log(3)(10))
  • lg(3*x+2*sqrt(x)-2)*1/(lg(5*x+3*sqrt(x)-3)3)>=(log(10)/log(27))/(log(10)/log(3)(10))
  • lg3*x+2*sqrtx-2*1/lg5*x+3*sqrtx-33>=log10/log27/log10/log310
  • lg(3*x+2*sqrt(x)-2)*1/(lg(5*x+3*sqrt(x)-3)³)>=(log(10)/log(27))/(log(10)/log(3)(10))
  • lg(3*x+2*sqrt(x)-2)*1/(lg(5*x+3*sqrt(x)-3) to the power of 3)>=(log(10)/log(27))/(log(10)/log(3)(10))
  • lg(3x+2sqrt(x)-2)1/(lg(5x+3sqrt(x)-3)^3)>=(log(10)/log(27))/(log(10)/log(3)(10))
  • lg(3x+2sqrt(x)-2)1/(lg(5x+3sqrt(x)-3)3)>=(log(10)/log(27))/(log(10)/log(3)(10))
  • lg3x+2sqrtx-21/lg5x+3sqrtx-33>=log10/log27/log10/log310
  • lg3x+2sqrtx-21/lg5x+3sqrtx-3^3>=log10/log27/log10/log310
  • lg(3*x+2*sqrt(x)-2)*1 divide by (lg(5*x+3*sqrt(x)-3)^3)>=(log(10) divide by log(27)) divide by (log(10) divide by log(3)(10))

  • Similar expressions

  • lg(3*x+2*sqrt(x)-2)*1/(lg(5*x+3*sqrt(x)+3)^3)>=(log(10)/log(27))/(log(10)/log(3)(10))
  • lg(3*x+2*sqrt(x)-2)*1/(lg(5*x-3*sqrt(x)-3)^3)>=(log(10)/log(27))/(log(10)/log(3)(10))
  • lg(3*x+2*sqrt(x)+2)*1/(lg(5*x+3*sqrt(x)-3)^3)>=(log(10)/log(27))/(log(10)/log(3)(10))
  • lg(3*x-2*sqrt(x)-2)*1/(lg(5*x+3*sqrt(x)-3)^3)>=(log(10)/log(27))/(log(10)/log(3)(10))
Solving inequalities/ lg(3*x+2*sqrt(x)-2)*1/(lg(5*x+3*sqrt(x)-3)^3)>=(log(10)/log(27))/(log(10)/log(3)(10))

lg(3*x+2*sqrt(x)-2)*1/(lg(5*x+3*sqrt(x)-3)^3)>=(log(10)/log(27))/(log(10)/log(3)(10)) inequation

A inequation with variable

The solution

You have entered [src] 
                           /log(10)\ 
    /          ___    \    |-------| 
 log\3*x + 2*\/ x  - 2/    \log(27)/ 
----------------------- >= ----------
   3/          ___    \    log(10)   
log \5*x + 3*\/ x  - 3/    -------*10
                            log(3)
$$\frac{\log{\left(\left(2 \sqrt{x} + 3 x\right) - 2 \right)}}{\log{\left(\left(3 \sqrt{x} + 5 x\right) - 3 \right)}^{3}} \geq \frac{\log{\left(10 \right)} \frac{1}{\log{\left(27 \right)}}}{10 \frac{\log{\left(10 \right)}}{\log{\left(3 \right)}}}$$ 
log(2*sqrt(x) + 3*x - 2)/log(3*sqrt(x) + 5*x - 3)^3 >= (log(10)/log(27))/((10*(log(10)/log(3))))
Detail solution
Given the inequality:
$$\frac{\log{\left(\left(2 \sqrt{x} + 3 x\right) - 2 \right)}}{\log{\left(\left(3 \sqrt{x} + 5 x\right) - 3 \right)}^{3}} \geq \frac{\log{\left(10 \right)} \frac{1}{\log{\left(27 \right)}}}{10 \frac{\log{\left(10 \right)}}{\log{\left(3 \right)}}}$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(\left(2 \sqrt{x} + 3 x\right) - 2 \right)}}{\log{\left(\left(3 \sqrt{x} + 5 x\right) - 3 \right)}^{3}} = \frac{\log{\left(10 \right)} \frac{1}{\log{\left(27 \right)}}}{10 \frac{\log{\left(10 \right)}}{\log{\left(3 \right)}}}$$
Solve:
$$x_{1} = 33.6096678407414$$
$$x_{1} = 33.6096678407414$$
This roots
$$x_{1} = 33.6096678407414$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 33.6096678407414$$
=
$$33.5096678407414$$
substitute to the expression
$$\frac{\log{\left(\left(2 \sqrt{x} + 3 x\right) - 2 \right)}}{\log{\left(\left(3 \sqrt{x} + 5 x\right) - 3 \right)}^{3}} \geq \frac{\log{\left(10 \right)} \frac{1}{\log{\left(27 \right)}}}{10 \frac{\log{\left(10 \right)}}{\log{\left(3 \right)}}}$$
$$\frac{\log{\left(-2 + \left(2 \sqrt{33.5096678407414} + 3 \cdot 33.5096678407414\right) \right)}}{\log{\left(-3 + \left(3 \sqrt{33.5096678407414} + 5 \cdot 33.5096678407414\right) \right)}^{3}} \geq \frac{\log{\left(10 \right)} \frac{1}{\log{\left(27 \right)}}}{10 \frac{\log{\left(10 \right)}}{\log{\left(3 \right)}}}$$
                        log(3)  
0.0333684186580993 >= ----------
                      10*log(27)

the solution of our inequality is:
$$x \leq 33.6096678407414$$
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       x1
Solving inequality on a graph
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