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2*log(24*x)=-5*log(4*x)-2 equation

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Numerical solution:

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The solution

You have entered [src]
2*log(24*x) = -5*log(4*x) - 2
$$2 \log{\left(24 x \right)} = - 5 \log{\left(4 x \right)} - 2$$
The graph
Rapid solution [src]
      5/7  -2/7
     6   *e    
x1 = ----------
         24    
$$x_{1} = \frac{6^{\frac{5}{7}}}{24 e^{\frac{2}{7}}}$$
x1 = 6^(5/7)*exp(-2/7)/24
Sum and product of roots [src]
sum
 5/7  -2/7
6   *e    
----------
    24    
$$\frac{6^{\frac{5}{7}}}{24 e^{\frac{2}{7}}}$$
=
 5/7  -2/7
6   *e    
----------
    24    
$$\frac{6^{\frac{5}{7}}}{24 e^{\frac{2}{7}}}$$
product
 5/7  -2/7
6   *e    
----------
    24    
$$\frac{6^{\frac{5}{7}}}{24 e^{\frac{2}{7}}}$$
=
 5/7  -2/7
6   *e    
----------
    24    
$$\frac{6^{\frac{5}{7}}}{24 e^{\frac{2}{7}}}$$
6^(5/7)*exp(-2/7)/24
Numerical answer [src]
x1 = 0.112597031849081
x1 = 0.112597031849081