1. ## 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.\

2. 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?

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

what does this tell you?

4. does it mean that x = 1?

5. 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?

6. 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.

7. 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?

8. 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.

9. 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?

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

Yep and it has no definative slope.

11. 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.

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

is that all i would have to say?

12. Just say f(x) is the linear function x=1

Use the logic shown in my first post to prove it.

13. 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?

14. Also another question. Why do you put it as 1^y ... isn't it 1^x. where does teh y come from?

15. Originally Posted by agent2421

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

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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