Question

Determinați n apartine N pentru care :
a)3^2n +17 ×3^3=9^25
b)(6^n)^4×36=216^10
c)15^n+4:5^n+4=81^6
d)81^n:9^n+9^n+2:9=90×9^6
e)(4^n+3)^2×8^n=32×(8^14)^2

Answer 1

a) 3²ⁿ⁺²⁰ = 3⁵⁰    2n + 20 = 50    2n = 30     n = 15
b) 6⁴ⁿₓ6² = 6³⁰     6⁴ⁿ⁺² = 6³⁰   4n + 2 = 30    n = 7
c) 3ⁿ⁺⁴ = 3²⁴    n+ 4 = 24    n = 20
d)  9ⁿ + 9ⁿ⁺¹ = 10ₓ9⁷    9ⁿ(1 + 9) = 10ₓ9⁷     10ₓ9ⁿ = 10ₓ9⁷     n = 7
e) 4²ⁿ⁺⁶ₓ2³ⁿ = 2⁵ₓ2⁸⁴      2⁷ⁿ ⁺¹² = 2⁸⁹    7n +12 = 89    7n = 77   n = 11