Which of the following is the solution to the equation 25^2c = square root of 5^(4c + 16) ?

Question

Which of the following is the solution to the equation 25^2c = square root of 5^(4c + 16) ?
Select one:
A. c = -5 over 2
B. c = 7 over 2
C. c = 4
D. c = -7/2

Answer 1

I'm going to assume that you mean 25^2c

In the future, please put parentheses around the 2c to make your question more legible.
e.g. 25^(2c).

25 = 5²

Therefore, we can substitute 5² for 25 and get:

(5²)^2c=sqrt [5^4c+16]

 

Using exponential laws, we get:

(5²)^2c = (5^4c+16)^1/2

5^4c = 5^2c+8

 

Therefore:

4c = 2c + 8
-2c   -2c

2c = 8

Divide both sides by 2 and c = 4.