Question

Which of the following is the solution to the equation √(5)^(8n)=125^(n+3)

Answer 1

n = 3
n = 9
n = -9
n = -3

Answer 2

9

Answer 3

Let's get the base same.

\(\Large \color{Black}{\Rightarrow (5^{1 \over 2})^{8n} = (5^3)^{n + 3}}\)

\(\Large \color{Black}{\Rightarrow 5^{4n} = 5^{3n + 9} }\)

Equate the exponents when base is same.

\(\Large \color{Black}{\Rightarrow 4n = 3n + 9 }\)
\(\Large \color{Black}{\Rightarrow n = 9 }\)