Question

HELLPPPP!!!! PLLLEEZZ!! :))
Which of the following is the solution to the equation sqrt5^8n = 125^(n + 5) ?
n=5,n=-5,n=15,n=-15?

Answer 1

\[ \large \sqrt{5}^{8n}=125^{n+5} \]
??

Answer 2

u can see here

http://www.wolframalpha.com/input/?i=sqrt5%5E8n+%3D+125%5E%28n+%2B+5%29

Answer 3

@helder_edwin yah thats right ;)

Answer 4

Ok first
\[ \large \sqrt{5}^{8n}=(5^{1/2})^{8n}=5^{1/2\cdot8n}=5^{4n} \]
OK?

Answer 5

yah!

Answer 6

then
\[ \large 125^{n+5}=(5^3)^{n+5}=5^{3(n+5)}=5^{3n+15} \]

Answer 7

so
\[ \large \sqrt{5}^{8n}=12^{n+5} \]
becomes
\[ \large 5^{4n}=5^{3n+15} \]

Answer 8

agree?

Answer 9

ok... but where did 12 come from?

Answer 10

sorrry 125 not 12

Answer 11

ok!! yah i understand so far! ;)

Answer 12

now we have this
\[ \large A^x=A^y\qquad\Rightarrow\qquad x=y \]

Answer 13

this means that
\[ \large 5^{4n}=5^{3n+15} \]
becomes
\[ \large 4n=3n+15 \]

Answer 14

u can finish this
right?

Answer 15

so its right?