Maths Solution to a equation

hey guys, does anyone know how to solve this: to isolate n

cos^n(0.18)=sqrt(2)

thanks

[Torsten]

Hint: Take log on both sides.

[Miguel Albuquerque]

I know the simplified solution, is there anyway to do log of base cos(x) in matlab?

[Torsten]

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]

n=real((1/2*log10(2))/(log10(cos(n))));

This is the answer by simplifying the equation

[Torsten]

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))

[Miguel Albuquerque]

yes I can

Answer 1

[KSSV]

syms n
eqn = cos(0.8)^n == sqrt(2) ;
s = solve(eqn,n)

s = 

vpa(s)

ans = 

[Miguel Albuquerque]

Thanks a lot :D