Solving for n. Logarithm How come: (3^n)/(2^(2n-1))<0.5*10^(-5) will be equal to n=45?

klastiesym

klastiesym

Answered question

2022-10-27

Solving for n. Logarithm
How come:
3 n 2 2 n 1 < 0.5 10 5
will be equal to n = 45?

Answer & Explanation

indivisast7

indivisast7

Beginner2022-10-28Added 13 answers

3 n 2 2 n 1 = 3 n 2 2 n 2 = 2 3 n 4 n = 2 ( 3 4 ) n < 1 2 10 5 ( 3 4 ) n < 1 4 10 5 n log ( 3 4 ) < log ( 10 5 4 ) Taking logarithm of both sides n > log ( 10 5 4 ) log ( 3 4 ) 44.8 Dividing by  log ( 3 4 )  which is negative
Hence, assuming n N , the minimal value of n that the inequality holds for is 45.

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