1. ## Logs

So my teacher has asked me...

to write ANY log function and answer these questions:
1. what is the domain?
2. what is the range?
3. at what interval is the function negative?
4. at what interval is the function positive?

But he didnt give us any examples so I dont really know what to do... if someone could provide me with an example on this that would be more then appreciated.

2. ## Re: Logs

for example :

$\displaystyle y=\log_2(x+1)$

1. domain

$\displaystyle x+1>0 \Rightarrow x\in (-1,+\infty)$

2. range

$\displaystyle y \in (-\infty,+\infty)$

3. y<0

$\displaystyle x \in(-1,0)$

4. y>0

$\displaystyle x \in(0,+\infty)$

3. ## Re: Logs

Hello, I'm a new user.

How can I solve this equation: log 8x-log(1+square root of x)=2? Explain me step by step how do you do it. Thanks.

4. ## Re: Logs

You should have learnt the following:

$\displaystyle log(a)+log(b)=log(ab)$

$\displaystyle log(a)-log(b)=log\left(\frac{a}{b}\right)$

$\displaystyle log_b a=c \iff b^c=a$

If you're going to be able to apply these (and others) you first need to learn them.

Also, it's better to start a new thread for a new question.

5. ## Re: Logs

I know that but I'm stuck where I have to write in general form.

6. ## Re: Logs

Well for a start you should apply $\displaystyle log(a)-log(b)=log\frac{a}{b}$. Post what you get.

7. ## Re: Logs

I get: log 8x/1+square root of x= 2, then I put base 10 on both sides.

8. ## Re: Logs

If I were not using LaTeX I'd use brackets, like this

log[ 8x / (1+sqrt(x) ) ] = 2

However LaTeX is easy..$\displaystyle \log\left(\frac{8x}{1+\sqrt{x}}\right)=2$

Yes, if this is base 10 you would then have $\displaystyle \frac{8x}{1+\sqrt{x}}=10^2$

Link to LaTeX help to follow..

9. ## Re: Logs

where is LaTex help? and yes I did what you did above, and what next?

11. ## Re: Logs

How do I use that?

12. ## Re: Logs

How do you use what?

13. ## Re: Logs

The LaTex Tutorial.

14. ## Re: Logs

Click where it says Latex.pdf and have a read.

15. ## Re: Logs

I dont know how to write substracting operations.