Help with inverse logarithm

I am attempting to solve a problem, but I cannot run my code because of an error. The code below is what I'm trying to run.

% Solve for life using SWT equations for a, b, and c.
Sa = 220; % Stress amplitude in MPa given in problem
Sm = 100; % Given stress as a matlab vector (MPa)
Smax = Sm + Sa; % Calculate maximum stress
b = -0.102; % Correction factor for material
N = ((log(b)\log(10))*((sqrt(Smax*Sa))\Sm))\2; % Lifefor mean stresses using SWT equation

The formula I'm trying to use is down below:

Also, I'm trying to figure out how to run the formula multiple times with different inputs of Sm. Such that Sm = 0, 100, and -100.

Any help will be greatly appreciated!

Answer 1

[Abel Corona]

Figured it out!

% Solve for life using SWT equations for a, b, and c.
Sa = 220; % Stress amplitude in MPa given in problem
Sm = [0 110 -110]; % Given stress as a matlab vector (MPa)
Sf = 900; % MPa
Smax = Sm + Sa; % Calculate maximum stress
b = -0.102; % Correction factor for material
N = (nthroot((sqrt(Smax*Sa)/Sf),b))/2; % Lifefor mean stresses using SWT equation

Answer 2

[KSSV]

Read about element by element operations in matlab.

% Solve for life using SWT equations for a, b, and c.
Sa = 220; % Stress amplitude in MPa given in problem
% Sm = 100; % Given stress as a matlab vector (MPa)
Sm = [0, 100, -100] ; 
Smax = Sm + Sa; % Calculate maximum stress
b = -0.102; % Correction factor for material
N = ((log(b)\log(10))*((sqrt(Smax.*Sa)).\Sm))\2; % Lifefor mean stresses using SWT equation