Question

Determinați numărul natural n din egalitatea:[(3/5)^6]^10=[(9/25)^5]^n
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Answer 1

Răspuns:

[(3/5)^6]^10=[(9/25)^5]^n

[(3/5)⁶]¹⁰=[(3²/5²)⁵]^n

(3/5)⁶˟¹⁰=[(3²/5²)⁵˟ⁿ

(3/5)⁶⁰=(3/5)²˟⁵˟ⁿ

(3/5)⁶⁰=(3/5)¹⁰˟ⁿ

60=10×n

n=60:10

n=6 aparține lui N