Question

Can someone help me please ?

Answer 1

25^(n-3)=5^(n+8)
Remember: 25=5²
Therefore:
5^[(n-3)²]=5^(n+8)
5^(2n-6)=5^(n+8)
Then:
2n-6=n+8
2n-n=8+6
n=14

Answer: n=14

Answer 2

25ⁿ ⁻ ³  =  5ⁿ ⁺ ⁸

Make both bases to be equal.

Recall 25 = 5²

(5²)⁽ⁿ ⁻ ³⁾  =  5ⁿ ⁺ ⁸

5²⁽ⁿ ⁻ ³⁾  =  5ⁿ ⁺ ⁸

2*(n - 3) = 2*n - 2*3 = 2n - 6

5²ⁿ ⁻ ⁶  =  5ⁿ ⁺ ⁸

Since the bases which is 5 are equal, that means the powers are the same.

2n - 6 = n + 8,    take the n to the left side of the equation

2n - n = 8 + 6

n = 14

I hope this helps.