How can I use fzero on these two functions?

I can't seem to get fzero to work on these two functions. I tried rearanging them to bring it to one side but it would not work. Please help me with this.

This is the code I have been trying to use for the second problem

f=@(x) (log(4*x-3))/-0.1

fzero(f,[0 4])

It then gives me this error

Error using fzero

Function values at interval endpoints must be finite and real.

Error in A3_SECTION_07_501178997_501160077 (line 6)

fzero(f,[0 4])

Answer 1

[John D'Errico]

Why in the name of god and little green apples do you want to transform the function, by taking the log? Just move the exponential to the right hand side, so fzero will be looking for a zero result.

First, verify a solution exists.

F2 = @(x) -exp(-0.1*x) + 4*x - 3;
fplot(F2,[0,4])
grid on

Clearly, one does, and it is near x==1.

fzero(F2,[0,4])

ans = 0.9767

[Hadi]

I put it into desmos and it was giving me a completly differnent graph so I thought it was wrong. It now makes sense though so thank you. (I will also be using your phrase "why in the name of god and little green apples" so much)

[John D'Errico]

Just a phrase I always liked. :-) It does seem to fit on Answers often enough.

Answer 2

[Torsten]

Use the original equation. Why do you take log on both sides - it only implies problems for x <= 3/4.

f = @(x)4*x-3-exp(-0.1*x);
x0 = fzero(f,[0 4])

x0 = 0.9767

f(x0)

ans = -1.1102e-16

Answer 3

[Matt J]

If you are going to transform the function, you must restrict the search to the domain where the transform is valid,

f=@(x) log(4*x-3)+0.1*x;
fzero(f,[3/4+eps,4])

ans = 0.9767