Question

exercitiul 13 va rogg

Answer 1

13.
a)2ⁿ⁺³=4¹¹ sau 2ⁿ⁺³=(2²)¹¹ sau 2ⁿ⁺³=2²²
    n+3=22 =>n=19
b)3²ⁿ⁺¹=9¹⁵:3 sau 3²ⁿ⁺¹=(3²)¹⁵:3 sau 3²ⁿ⁺¹=3³⁰:3 sau 3²ⁿ⁺¹=3²⁹
   2n+1=29 =>n=15
c)7³ⁿ⁻¹=49²² sau 7³ⁿ⁻¹=(7²)²² sau 7³ⁿ⁻¹=7⁴⁴
   3n-1=44 =>n=15
d)2ⁿ:2⁶=2⁹ sau 2ⁿ⁻⁶=2⁹
   n-6=9 =>n=15
e)3²ⁿ⁺⁷·3³=9¹⁵ sau 3²ⁿ⁺¹⁰=(3²)¹⁵ sau 3²ⁿ⁺¹⁰=3³⁰
   2n+10=30 =>n=10
f)(5ⁿ)⁴·25=125¹⁰ sau 5⁴ⁿ·5²=(5³)¹⁰ sau 5⁴ⁿ⁺²=5³⁰
   4n+2=30 =>n=7
g)5ⁿ²:5=25²⁴ sau 5ⁿ²:5=(5²)²⁴ sau 5ⁿ²⁻¹=5⁴⁸
   n²-1=48 =>n²=49 =>n=+/-7
h)3ⁿ⁺¹·3²ⁿ⁺²=27¹¹ sau 3⁽ⁿ⁺¹⁺²ⁿ⁺²⁾=(3³)¹¹ sau 3³ⁿ⁺³=3³³
  3n+3=33 =>n=10
i)15ⁿ⁺²:5ⁿ⁺²=9¹⁰ sau (5·3)ⁿ⁺²:5ⁿ⁺²=(3²)¹⁰ sau 3ⁿ⁺²=3²⁰
   n+2=20 =>n=18