Question

Can anyone help me out with logarithms? I have a benchmark coming up and am so not ready! Thanks!

Answer 1

What do you need help with?

Answer 2

I can figure out the simple things, but usually when it gets to a natural logarithm or possibly graphing, im hopeless

Answer 3

A natural log is just \(log_e\), that is, the log base e. It's kind of a strange base to try to grasp intuitively but it works the same as every other log if you understand the basic concept.

You can solve equations like \(2^n = 256\), right?

Answer 4

Yea, I can do that. n=8

Answer 5

correct?

Answer 6

Yes. :)
So a natural log is just what you'd use to solve something like\[e^n = x\]
It's just \(n = \ln x\)

(If you already get this part, then we can move on. I'm not totally sure what part you're having trouble with yet)

Answer 7

What youre saying is making sense

Answer 8

Can i just list off what he said would be on the benchmark that is confusing me?

Answer 9

Ok

Answer 10

-Use properties of log to expand/condense
-solve exponential equations that require logs
-graph a function with given information
-compositions to prove if two things are inverse

Answer 11

Well, we did the second thing already. :D

Answer 12

oh yea, haha

Answer 13

If you know the properties of exponents, then all you have to do is remember \(\log_x x^n = n\) and you can think of the properties of logs.

For example, \(\log xy = \log x + \log y\). You know this because \(x^a \times x^b = x^{a + b}\) which also means that \(\log_x (x^ax^b) = \log_x x^{a + b} = a + b\)

Answer 14

i remember him saying that, along with \[\log{x} -\log{y} =\log{\frac{ x }{ y }} \]

Answer 15

Right, that's another one! Directly connected to the fact that \(\frac{x^a}{x^b} = x^{a-b}\)

Answer 16

ok, i took notes on the properties (i just found them xD) now i know how to graph an exponential function but not a log

Answer 17

I think all you really have to do to graph a log is to plot points at the nice round values and then draw a curve between them. At least that's all I know how to do. :D

Answer 18

ehhh wouldnt there only be one value tho? haha

Answer 19

What do you mean?

Answer 20

doesn't a log only have one value? SO how could you plot two?

Answer 21

I'm talking about graphing a function like \(y = \log x\)

Answer 22

yea, for an exponential, the two points would be (0,1) and (1,A), A being the base

Answer 23

For a log it'd work the other way.
I mean, this is basically what a log means.

So for \(y = log_{10} x\) you could plot a point at (1, 0) like always, then one at (10, 1), and one at (100, 2), and (1000, 3) and so on. I hope you have a lot of graph paper... :P

Answer 24

Haha proooobably not xD, so a log graph looks no different then an exponential one?

Answer 25

Here's what the graph of the (base 10) log looks like.
http://www.wolframalpha.com/input/?i=graph+y+%3D+log_10+x

You can ignore the orange line if you don't care about imaginary numbers, which you probably don't right now.

Answer 26

So it is different

Answer 27

I feel like such an idiot right now

Answer 28

But related. Remember the definition of log.
Saying \(y = \log_a x\) is the same as saying \(x = a^y\)

Answer 29

That's why (1, B) is on the exponential graph and (B, 1) is on the log graph.
(Where B is the base)

Answer 30

but the shouldnt the graph for \[y=\log_{} x\] have points for (0,1) and (1,10)?

Answer 31

No. In the case of (1, 10), x = 1 and y = 10.
And \(\log 1 \ne 10\).

Answer 32

Oh, I just saw your other reply

Answer 33

I might have to call this meeting adjourned, Im not much of a studious person xD

Answer 34

Remember, \(y = \log_a x\) is the same as \(x = a^y\), so if you can do exponentials, just do it backwards.

Answer 35

Alright, makes sense :)