Question

% MATLAB contains functions to calculate the natural logarithm (log), the
% logarithm to the base 10 (log10), and the logarithm to the base 2
% (log2). However, if you want to find a logarithm to another base - for
% example, base b - you'll have to do the math yourself with the formula

% y = logb(x,b)
y = log10(4)./log10(2)

% What is the logb of 10 when b is defined from 1 to 10 in increments of
% 1?

l = 1:1:10;

% L = logb(x,b)
L = log10(x)./log10(l)

Answer 1

on the 2nd part.

Answer 2

@zepdrix

Answer 3

l is a vector

Answer 4

so... what's the question? again

Answer 5

and yes, if you're referring to other log bases, you'd need to use the "change of base rule" \(\Large log_{\color{red}{ a}}{\color{blue}{ b}}\implies \cfrac{log_{\color{olive}{ c}}{\color{blue}{ b}}}{log_{\color{olive}{ c}}{\color{red}{ a}}}\)

where "c" can be anything, so long, is the same above and below
so, you can use "e" or base 10

Answer 6

2 = log10(x) <==> 0 = log2(x)

I am trying to understand the math here.

Answer 7

wait does base refer to c or b or a?

Answer 8

base is the "subscript" letter dropped down

Answer 9

okay so the two equations above are equal? Because when we have logb(x) = log10(4)/log10(2) = 2

Answer 10

logb(x) = 2

Answer 11

exactly what are you trying to understand?

Answer 12

still trying to understand logb(x) = log(4)/log(2) ?

that is 2, but does the 2 represent the new basis for logb(x)?

Answer 13

it would be clearer if you wrote log_b(x) to mean log base "b"
then the formula would be log(x)/log(b)
where log is a "known" base (i.e. "e" or 10)

Answer 14

% What is the logb of 10 when b is defined from 1 to 10 in increments of
% 1?

Answer 15

well, bear in mind that, when the base is skipped, "10" is assumed
so log(x) really means \(\bf log_{10}(x)\)

so \(log_{\color{red}{ a}}{\color{blue}{ b}}\implies \cfrac{log_{\color{olive}{ c}}{\color{blue}{ b}}}{log_{\color{olive}{ c}}{\color{red}{ a}}}
\\ \quad \\ \quad \\
log_{\color{red}{ 4}}{\color{blue}{ 2}}\implies \cfrac{log{\color{blue}{ (2)}}}{log{\color{red}{ ( 4)}}}\implies
\cfrac{log_{\color{olive}{ 10}}{\color{blue}{ (2)}}}{log_{\color{olive}{ 10}}{\color{red}{ ( 4)}}}\)

Answer 16

Inf 3.3219 2.0959 1.6610 1.4307 1.2851 1.1833 1.1073 1.0480 1.0000

Answer 17

Are they saying b is the vector? b = 1:1:10

Answer 18

am I looking for another logarithm when the bases b = 1:1:10

Answer 19

yes, they are for different bases (though why they ask for base 1 is a bit mysterious, because we can't do base 1)

Answer 20

but I was making a vector so b = starting:increment:ending

Answer 21

% What is the logb of 10 when b is defined from 1 to 10 in increments of
% 1?

be is defined as a matrix

Answer 22

yes, I did
>> aa= logb(10,1:10)
aa =

Columns 1 through 9:

Inf 3.3219 2.0959 1.6610 1.4307 1.2851 1.1833 1.1073 1.0480

Column 10:

1.0000

Answer 23

I forgot about that...

Answer 24

**% What is the logb of 10 when b is defined from 1 to 10 in increments of
% 1?**

I interpret that to mean they want
\[ \log_1(10), \log_2(10), \log_3(10), ...\]

Answer 25

that makes sense. I interpreted it wrong.=/

Answer 26

you did it correctly up top
***
l = 1:1:10;

% L = logb(x,b)
L = log10(x)./log10(l)
****

Answer 27

what you are saying is logb(10, 1:10) is the same as what I did on the top but using another method?

Answer 28

though I would stay away from variables l (looks too much like 1, and some day you will regret it)

ii would be better
or even
log10(x) ./ (1:10)

Answer 29

did you create logb.m file that contains the lines
% y = logb(x,b)
% returns log_base_b(x)
function y= logb(x,b)
y= log(x)./log(b);

?

Answer 30

I will keep that in mind. I used "l" because I was thinkg L = l but I will be sure to stay away from l since it looks like 1

Answer 31

log10(x) ./ (1:10) <==== does it automatically know it's incrementing by one?

Answer 32

yes, you can test it. type 1:10 return in matlab

Answer 33

why do i need did you create logb.m file that contains the lines
% y = logb(x,b)
% returns log_base_b(x)
function y= logb(x,b)
y= log(x)./log(b);

Answer 34

oh so function y = logb(x,b) is a function huh?

Answer 35

function Add new function.
New functions may be added to MATLAB's vocabulary if they
are expressed in terms of other existing functions. The
commands and functions that comprise the new function must
be put in a file whose name defines the name of the new
function, with a filename extension of '.m'. At the top of
the file must be a line that contains the syntax definition
for the new function. For example, the existence of a file
on disk called STAT.M with:

function [mean,stdev] = stat(x)
%STAT Interesting statistics.
n = length(x);
mean = sum(x) / n;
stdev = sqrt(sum((x - mean).^2)/n);

defines a new function called STAT that calculates the
mean and standard deviation of a vector. The variables
within the body of the function are all local variables.
See SCRIPT for procedures that work globally on the work-
space.

A subfunction that is visible to the other functions in the
same file is created by defining a new function with the function
keyword after the body of the preceding function or subfunction.
For example, avg is a subfunction within the file STAT.M:

Answer 36

I assume that is what they want. You don't have to for this simple problem, but it's not hard to do, and it's convenient

Answer 37

okay. I didn't know about this command until now.

Answer 38

% y = logb(x,b)
% returns log_base_b(x) <==== this is a comment?
function y= logb(x,b)
y= log(x)./log(ii);


^^^I used this code letting ii = 1:1:10

It is not working

Answer 39

what does it do?

Answer 40

did you create a file named logb.m ?

Answer 41

% What is the logb of 10 when b is defined from 1 to 10 in increments of
% 1?

% L = logb(x,b)
ii = 1:1:10;
function y = logb(x,b)

L = log10(x)./log10(ii)

^^^This is what I have now


Error: File: Homework2.m Line: 15 Column: 2
Function definitions are not permitted in this context.

Answer 42

No I didn't create a file name logb.m Why does it need it's own file?

Answer 43

yes, you need a complete separate file (with that name) in the local directory
matlab has a search path to look for file names, and it will start by looking in your local director. (the one you see if you do dir )

Answer 44

I am writing all of this in a script btw

Answer 45

not in the command window

Answer 46

that's ok. the script will have its own file, with a name like homework.m

Answer 47

so I need to make a complete separate script with this info

% y = logb(x,b)
% returns log_base_b(x)
function y= logb(x,b)
y= log(x)./log(b);

and then go back to homework.m to run the new function? So the function command has to have its own m file huh?

Answer 48

yes. try it

Answer 49

Error: File: Homework2.m Line: 15 Column: 2
Function definitions are not permitted in this context.

Answer 50

Okay so I made a new script named logb(x) with this info in int
% y = logb(x,b)
% returns log_base_b(x)
function y= logb(x,b)
y= log(x)./log(b);

Then I went back to the other m file called homework2 which has this info

% What is the logb of 10 when b is defined from 1 to 10 in increments of
% 1?

% L = logb(x,b)
ii = 1:1:10;
function y = logb(x,b);

L = log10(x)./log10(ii)

Answer 51

the new file should be called logb.m


and in your script you type
logb(10,2)
for example

Answer 52

which script homework? Let me go back and rename the file logb

Answer 53

don't forget the .m extension

Answer 54

it automatically puts the .m at the end after renaming it logb

Answer 55

ok, now in your homework script
you can put in
logb(10,2)
to calculate log_2(10)
as a test, also put in log2(10)

Answer 56

Error in Homework2 (line 15)
logb(10,2)

Answer 57

% What is the logb of 10 when b is defined from 1 to 10 in increments of
% 1?

% L = logb(x,b)

logb(10,2)
log2(10)

^^^in homework2 script


% y = logb(x,b)
% returns log_base_b(x)
function y= logb(x,b)
y= log(x)./log(b);

^^^in logb.m script

Answer 58

in your command window, type
which logb

Answer 59

which logb
logb is a variable.

Answer 60

type
clear logb

Answer 61

okay said clear logb and then i ran the program still getting an error

Answer 62

perhaps you are setting logb inside your script?

if you do
dir
do you see the logb.m file ?

if you put
clear logb
logb(10,2)
in your command window, does it work ?

Answer 63

%% 3.2
% MATLAB contains functions to calculate the natural logarithm (log), the
% logarithm to the base 10 (log10), and the logarithm to the base 2
% (log2). However, if you want to find a logarithm to another base - for
% example, base b - you'll have to do the math yourself with the formula

% y = logb(x,b)
%y = log10(4)./log10(2)

% What is the logb of 10 when b is defined from 1 to 10 in increments of
% 1?

% L = logb(x,b)

log(10,2)
log2(10)

Answer 64

This is what I have in my script. I surpressed the %y = log10(4)./log10(2) because that was from the last question.


>> logb(10,2)
Undefined function or variable 'logb'.

Did you mean:
>> log(10,2)
Index exceeds matrix dimensions.

^^^What I get when I type logb(10,2) in command window

Answer 65

ok, in the command window, type
which logb

Answer 66

>> which logb
'logb' not found.

Answer 67

now type
dir

Answer 68

. RStudio.lnk
.. Shortcut to SecureDownloadManager.exe.lnk
.RData desktop.ini
Dropbox.lnk

Answer 69

it looks like you are not in the directory where you put logb.m

Answer 70

>> dir

. Homework1.m lab02.m weather_data.xls
.. Homework2.m logb.m.m

Answer 71

ok, that looks better. I would rename logb.m.m to logb.m

Answer 72

>> Homework2
Index exceeds matrix dimensions.

Error in Homework2 (line 15)
log(10,2)

Answer 73

yes log(10,2) is wrong. log is a matlab function and it only wants 1 number
logb(10,2) should work

but first,
which logb
does that find logb ?

dir
does that show logb.m file

>> logb(10,2)
does that work ?

Answer 74

>> Homework2

ans =

3.3219


r =

0.9000

Answer 75

Ignore the r

Answer 76

% What is the logb of 10 when b is defined from 1 to 10 in increments of
% 1?

% L = logb(x,b)

logb(10,2)

log2(10)


>> Homework2

ans =

3.3219


ans =

3.3219

Answer 77

That is pretty neat.

Answer 78

success

now you can do
logb(10,1:10)

Answer 79

ans =

Columns 1 through 9

Inf 3.3219 2.0959 1.6610 1.4307 1.2851 1.1833 1.1073 1.0480

Column 10

1.0000

Answer 80

one last question in logb(10,1:10) the (base, first, end)

Answer 81

does the first 10 represent the base?

Answer 82

no, the 10 is x in
\[ \log_b(x) \]
the 1:10 are the bases

Answer 83

okay got it.

Answer 84

if you save the answer
aa= logb(10, 1:10)
then
(1:10).^aa
should return 10's (except for the first one)

Answer 85

yep it return to 10. Well I am out. Thanks for showing me how to use the command function. I will probably have to use that command later in this course. later