How Are Expressions Derived from Previous Equations in Mathematical Problems?

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The discussion focuses on deriving mathematical expressions from previous equations, specifically how expressions 7 and 8 are achieved from equation 6, and expressions 13, 14, and 15 from equation 12. The method involves dividing equation 6 by B*η, applying exponentiation, simplifying, and renaming variables, such as changing γ to γthD. For expression 8, the variable R is substituted with 2R. The second problem requires additional formulas not provided in the referenced image.

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Problem number 1:
How the author has achieved expression 7 and 8 by using 6?

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Problem number 2:
How the author has achieved expression 13,14 and 15 by using 12?

jyMcl9H.png


Thanks in advance
 
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Just arithmetics. Divide (6) by B*η, put both sides in an exponent (2^...), simplify, rename γ to γthD.
To get (8), replace R by 2R.

I think the second problem needs some formulas not given in the image.
 

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