You cannot directly access a class without a reference to an instance of that class. Your best bet might be something like this:
Module Module1
Private m_MyForm As Form1
Public ReadOnly Property MyForm() As Form1
Get
If IsNothing(m_MyForm) Then m_MyForm = New Form1
Return m_MyForm
End Get
End Property
Public Sub WriteLog(ByVal txt As String)
MyForm.TextBox3.Text += txt + vbNewLine
End Sub
End Module
Now anywhere in your application you can access Form1 using Module1.MyForm.