Question

What value of n makes the equation true ? Show your work.

Answer 1

n = 6

Explanation:

Given the expression

`((19^8)/(7^n))^4 = ((19^4)/(7^3))^8 \\(19^(32))/(7^(4n)) = (19^(32))/(7^(24))\\(1)/(7^(4n)) = (1)/(7^(24)) \\Reciprocate \ both \ sides\\7^(4n) = 7^(24)\\4n = 24\\n = (24)/(4)\\n = 6`

Hence the value of n is 6