# Homework Help: Evaluate lim of f.

1. Feb 17, 2012

### mathlike

1. The problem statement, all variables and given/known data[/b]

Evaluate lim x goes to ∞ positive
((x-1)*(bx-1)/(b-1))(1/x)

2. Relevant equations

3. The attempt at a solution[/b]
I try to take log but it does not seem to work

Last edited: Feb 17, 2012
2. Feb 17, 2012

### DivisionByZro

Is this the problem?

$$\lim_{x\to\infty}\frac{(b^{x}-1)}{x(b-1)}^{\frac{1}{x}}$$

3. Feb 18, 2012

### mathlike

Yes. I tried taking log but to no avail

4. Feb 18, 2012

### alanlu

5. Feb 18, 2012

### mathlike

still cannot solve it. Need help guys! Appreciated.

6. Feb 18, 2012

### alanlu

To clarify, is it this?
$$\lim_{x\to\infty}\left(\frac{b^{x}-1}{x(b-1)}\right)^{\frac{1}{x}}$$
Or is it this?
$$\lim_{x\to\infty}\frac{(b^{x}-1)^{\frac{1}{x}}}{x(b-1)}$$

For the latter, note that for all x > 1, b > 1,
$$0 \leq (b^{x}-1)^{\frac{1}{x}} \leq b$$
For the former, I am not immediately sure.

Last edited: Feb 18, 2012
7. Feb 18, 2012

### Dick

Judging by you initial parentheses I think you actually mean. $$\lim_{x\to\infty} \big( \frac{b^{x}-1}{x(b-1)} \big) ^{\frac{1}{x}}$$.

And can you show why taking the log isn't working. Or something?

8. Feb 19, 2012

### mathlike

I simplified it down to calculate
limx->infinity (b^x-1)/x
......can help me to proceed?

9. Feb 19, 2012

### Dick

I don't see how you got that. You need to show us.