Question #7d0d9

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Answer 1 · 2017-05-27T15:12:01

$n = 1$

I'm going to assume the question is $5^(n + 1) = sqrt(25^(3n - 1))$

Square both sides to get:

$(5^(n + 1))^2 =(sqrt(25^(3n - 1)))^2$

Use $(a^n)^m = a^(nm)$

$5^(2n + 2) = 25^(3n - 1)$

$5^(2n + 2) = (5^2)^(3n - 1)$

$5^(2n + 2) = 5^(6n - 2)$

$2n + 2 = 6n - 2$

$4 = 4n$

$1= n$

Hopefully this helps!

Answer 2 · 2017-05-27T15:56:09

$color(brown)(n=1$

$5^(n+1)=(sqrt25)^(3n-1)$

$:.5^(n+1)=5^(3n-1)$

base numbers are the same then:

$:.n+1=3n-1$

$:.n-3n=-1-1$

$:.-2n=-2$

multiply both sides by $-1$

$:.2n=2$

$:.color(brown)(n=1$