Logarithmic Functions

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• Oct 21st 2009, 02:44 PM
agent2421
Logarithmic Functions
Can someone help me out with this question.

Explain what happens to the graph of the function f(x) = logbx when b is equal to 1.

I'm new to logarithmic function's and don't really understand it. Also if anyone can provide me with an online calculator to do these questions it'd be great.\
• Oct 21st 2009, 02:52 PM
stapel
Convert the logarithmic formula, y = log_b(x), into the equivalent exponential form, given that b = 1. What do you get?

Is it very interesting and useful, or is it kinda pointless? (Wink)
• Oct 21st 2009, 02:52 PM
pickslides
\$\displaystyle y = log_1x \Rightarrow 1^y =x \$

what does this tell you?
• Oct 21st 2009, 02:54 PM
agent2421
does it mean that x = 1?
• Oct 21st 2009, 02:59 PM
stapel
So what do you get as a function? "1^y = 1, so y = 1^1 = 1". Is this particularly useful? Is the graph particularly interesting?

So is it likely that you're going to be dealing with logs having a base of 1 any time soon? (Wink)
• Oct 21st 2009, 03:03 PM
agent2421
maybe I"m stupid or somethin lol but I still don't understand what your trying to say... I still don't know how to explain my opening question.
• Oct 21st 2009, 03:05 PM
stapel
What do you get when you plug "1" in for "x"? What do you get when you swap the exponential form back to the log form? What does your graph look like?
• Oct 21st 2009, 03:12 PM
agent2421
is there any online graphing calculator that would help me graph it,.... that's another problem because I don't know how it would look like.
• Oct 21st 2009, 03:22 PM
agent2421
I'm not sure if this is right or not but is it:

the graph is a straight line passing through the origin and having the slope =1 when b is = to 1?
• Oct 21st 2009, 03:42 PM
pickslides
Quote:

Originally Posted by agent2421
does it mean that x = 1?

Yep and it has no definative slope.
• Oct 21st 2009, 03:46 PM
agent2421
okay so to conclude... what is the best way to answer the question? If i'm supposed to show work how should I Do so? I'm not going to lie but this of course is homework but my teacher in school doesn't really explain it well.... in fact he's a history teacher and fisrt year teaching math.... so basically I don't understand much when he teaches it.

---

When b is = to 1, the x intercept is 1 and there is no definative slope...

is that all i would have to say?
• Oct 21st 2009, 03:49 PM
pickslides
Just say f(x) is the linear function x=1

Use the logic shown in my first post to prove it.
• Oct 21st 2009, 04:09 PM
agent2421
Quote:

Originally Posted by pickslides
\$\displaystyle y = log_1x \Rightarrow 1^y =x \$

what does this tell you?

thanks a lot. So basicalily I just used your answer but I added another step after the log_1x

y =\$\displaystyle log_1x \$
1^y =x
x = 1

Therefore f (x) is always the linear function x = 1

*note: 1^y will ALWAYS be = to 1. (ex: 1*1*1*)

Do you think I'll get full marks for this answer?
• Oct 21st 2009, 04:12 PM
agent2421
Also another question. Why do you put it as 1^y ... isn't it 1^x. where does teh y come from?
• Oct 21st 2009, 04:27 PM
pickslides
Quote:

Originally Posted by agent2421

Do you think I'll get full marks for this answer?

Quote:

Originally Posted by agent2421

Why do you put it as 1^y ... isn't it 1^x

no, \$\displaystyle x=1 \neq x^1\$

using log laws

\$\displaystyle a = log_bc \Rightarrow b^a =c\$

So

\$\displaystyle y = log_1x \Rightarrow 1^y =x\$
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