0 个投票

hey guys, does anyone know how to solve this: to isolate n
cos^n(0.18)=sqrt(2)
thanks

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Torsten
Torsten 2022-5-10
Hint: Take log on both sides.
Miguel Albuquerque
Miguel Albuquerque 2022-5-10
I know the simplified solution, is there anyway to do log of base cos(x) in matlab?
Torsten
Torsten 2022-5-10
What is the "simplified solution" ?
You can take logs to any basis on both sides and get the correct solution:
n * log10(cos(0.18)) = log10(sqrt(2))
n * log(cos(0.18)) = log(sqrt(2))
n * log2(cos(0.18)) = log2(sqrt(2))
and so on.
Miguel Albuquerque
Miguel Albuquerque 2022-5-10
编辑：Miguel Albuquerque 2022-5-10
n=real((1/2*log10(2))/(log10(cos(n))));
This is the answer by simplifying the equation
Torsten
Torsten 2022-5-10
Can't you solve these equations for n ?
n * log10(cos(0.18)) = log10(sqrt(2))
n * log(cos(0.18)) = log(sqrt(2))
n * log2(cos(0.18)) = log2(sqrt(2))

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 采纳的回答

KSSV
KSSV 2022-5-10
Ran in:

0 个投票

Ran in:
syms n
eqn = cos(0.8)^n == sqrt(2) ;
s = solve(eqn,n)
s = 
vpa(s)
ans = 

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