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1/8*sqrt(2^x-1)=4^-1.25 equation

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Numerical solution:

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The solution

You have entered [src]
   ________       
  /  x            
\/  2  - 1     1  
----------- = ----
     8         5/4
              4   
$$\frac{\sqrt{2^{x} - 1}}{8} = \frac{1}{4 \sqrt{2}}$$
The graph
Rapid solution [src]
     log(3)
x1 = ------
     log(2)
$$x_{1} = \frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
x1 = log(3)/log(2)
Sum and product of roots [src]
sum
log(3)
------
log(2)
$$\frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
=
log(3)
------
log(2)
$$\frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
product
log(3)
------
log(2)
$$\frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
=
log(3)
------
log(2)
$$\frac{\log{\left(3 \right)}}{\log{\left(2 \right)}}$$
log(3)/log(2)
Numerical answer [src]
x1 = 1.58496250072116
x2 = 1.58496250072116
x2 = 1.58496250072116