Math Is Fun Forum

CIV

Member

Registered: 2014-11-09

Posts: 74

Logarithms. What's the deal?!?!?!?

The book I'm using for class drags! It was OK all the way up until chapter 4. Section 4.1 was about natural e and it was a bit blah explaining natural e but I think I know about e for now. Section 4.2 is where I am at now and I just don't get it. It's about Logarithms. I understand the concept but there is no mathematical or algebraic explanation on how to solve it. In the book and even this website basically tells you to just take a shot in the dark or scribble the hell out of a sheet of paper to find the exponent. For instance, on this site, the example is:

The same with this example:

The explaination:

WELL, 1/8 = 0.125

Well what?!?!?! What if I didn't know that? They are not all that easy! Here's one from the book that I have been trying to figure out a method for:

I know the answer is 3/4, but do I solve to get that?!?!? Other than using trial and error. This is as far as I got to understanding how to solve for it:

I see a 4 and a 3. This makes me think I'm close, but I I can figure out how it's solved for 3/4. Can someone please explain to me how to solve these problem without using shot in the dark trial and error? Thank you. I have been working on this for 2 days now and I'm tired. I have to move on but I don't understand this.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Logarithms. What's the deal?!?!?!?

hi CIV,

I think this method will work for these:

Change the log expression back to a power expression.
'Re-log' it but using a more 'helpful' log base.
Simplify.

eg.

Let

A 'helpful' log base now would be base 8.

Now simplify.  The log of 8 in base 8 is just 1.  What power must I raise 8 to, so that I get 16 ?  Both 8 and 16 are powers of 2, so I can first make 2 then make 16;   ie. cube root 8 and then take the fourth power.

eg.

In this case we can see that base 5 was OK to start with .  What power must I raise 5 to, so that I get  1/125.  I need to cube 5 and take the reciprocal:

Note: this is not quite what you wrote in your opening line.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

CIV

Member

Registered: 2014-11-09

Posts: 74

Re: Logarithms. What's the deal?!?!?!?

Thank you for your help, but It still looks like something I would have to trial and error to solve. Meaning no easy way to do it. I skipped ahead in my book to see if there was anything it was going to teach me that I could use in the earlier section. I saw the changing of the log formula, which is what you are doing, but still... what power do I have to raise 8 to get 16 or whats the root of 16 to get 8? That's it. You kind of just have to play around to get the answer. Its very fortunate the 8 and 16 have the same base of 2, 2 being an even more helpful base to use, but what if two numbers don't so easily have the same base? I mean you can give them the same base but... I don't think it helps for many. This really drags. I did so well up until this point.

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

Website

Re: Logarithms. What's the deal?!?!?!?

what power do I have to raise 8 to get 16 or whats the root of 16 to get 8? That's it. You kind of just have to play around to get the answer.

. No trial and error involved.

CIV

Member

Registered: 2014-11-09

Posts: 74

Re: Logarithms. What's the deal?!?!?!?

I think I'm starting to understand this. I had to skipp ahead several sections before it actually started to teach how to do this. What a very poor way of teaching. Frustate the hell out of the student as a sick joke before teaching. This is more what I was looking for:

I guess I was looking more for an algebraic way. Not that what you were showing me wasn't algebraic, wanted to see it worked out like this so I can get a clear mental picture of whats going on. I was literally doing the problem for section 4.4 before the problems in section 4.2. Can you believe that? Why would they do that? Just horrible.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Logarithms. What's the deal?!?!?!?

Hi;

It is incorrect to always seek an algebraic method as a solution for every type of equation. When there is one we are happy but they are rare. The hard fact is most equations can not be solved by algebra, usually iteration is used and this starts off with a guess!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

CIV

Member

Registered: 2014-11-09

Posts: 74

Re: Logarithms. What's the deal?!?!?!?

Hi;

It is incorrect to always seek an algebraic method as a solution for every type of equation. When there is one we are happy but they are rare. The hard fact is most equations can not be solved by algebra, usually iteration is used and this starts off with a guess!

Ugh, that drags, but there is always a way to solve something. An official method. Instructions. I know that guessing is a thing with mathematics, but there's always an explanatory way of doing the math. Thanks for you help. I fully understand this now. Got more than half of my homework done early early this morning, and it only took me about 45 minutes once i had it down good.