Finding a single root of x^(3.6)=75

Hi, the question is to use MATLAB to determine the real root of x^3.6 = 75. I thought I could use the fzero code and wrote this code below but I keep getting an error and can't figure out why or if this is how I should approach this question.

fun = x^(3.6)-75;

x0=3;

z = fzero(fun,x0)

can anyone help?

[Benjamin Thompson]

Can't you take the ln of both sides, simplify into a addition problem, and solve for ln(x)?

https://www.mathsisfun.com/algebra/exponents-logarithms.html

[James Tursa]

FYI, when you post "... I keep getting an error ..." it is best to copy & paste the entire error message in your question so that we don't have to guess what the error is.

[Sarah Elena Aiko Johnson]

okay thank you! Im new to the forum.

Answer 1

[James Tursa]

Make a function handle with the @ operator. E.g.,

fun = @(x)  x^(3.6)-75;
x0=3;
z = fzero(fun,x0)

z = 3.3178

Check

z^3.6

ans = 75

Or you can raise both sides of original equation to (1/3.6) power to solve for x directly.

Or you can solve directly using log( ) function as Benjamin suggests. (Followed up by using the exp( ) function)

[Steven Lord]

There are also the nthroot and realpow functions.

nthroot(75, 3.6)

ans = 3.3178

realpow(75, 1/3.6)

ans = 3.3178