This requires these two principles of exponents

(1)     =   <--The reversal of adding exponents

(2)     =  <--The reversal of the power of a fraction 


 -  = 

Divide through by 

 - 5 = 

Use principle (2) on the left side
Write 6 as 2*3 on the right

 - 5 = 

Use principle (1) on the right side

 - 5 = 

Use principle (1) on the left
Subtract exponents of 2 on the right

 - 5 = 

Simplify

 - 5 = 

Swap factors on the left, use principle (1) on the right denominator

 - 5 = 

Remove the 1 exponent

 - 5 = 

Multiply through by 2

 - 2·5 = 

 - 10 = 

 - 10 = 

 - 10 = 

 -  - 10 = 0

let u = 

Then u² =  = 

Then we have

3u² - u - 10 = 0

Factoring,

(u - 2)(3u + 5) = 0

Use the zero-factor principle:

u - 2 = 0;  3u + 5 = 0
    u = 2       3u = -5
                 u = 

Use u = 2

Since u = 

 = 2

Take logs of both sides:

 = 

Use the principle 

 = 

Divide both sides by 

 =  = 1.709511291

That's the only solution because if we try 

u = 

 = 

That cannot produce an additional solution because because  is
positive and a positive number raised to any power, positive or negative,
gives a positive answer. 

Edwin