# Logarithmic functions

1. Jan 26, 2005

### Erin_Sharpe

y = logx 4

identify the domain and range

state whether the function is increasing or decreasing, and identify the vertical asympotote, teh x-intercept and the value of x at y = 1

I need some help!

2. Jan 26, 2005

### mathman

The 4 in your expression appears to be hanging out in space. It would be helpful if you could write the equation more clearly.

3. Jan 26, 2005

### dextercioby

$$y(x)=\log_{x} 4$$

Can you determine the domain and range...??

Discuss the sign of its derivative...

Daniel.

P.S.Can u solve the equation y(x*)=1??Find x*...

4. Jan 26, 2005

### HallsofIvy

Staff Emeritus
I believe that loga(x) is only defined for a> 0. Does that help.

5. Jan 26, 2005

### Zurtex

Also I don't think that loga(x) is defined for a=1.

6. Jan 27, 2005

### dextercioby

Write
$$y(x)=\frac{\ln 4}{\ln x}$$

Cau u see now what is the range??What about the domain?

Daniel.

7. Jan 27, 2005

### Erin_Sharpe

See I thought x was 2??

8. Jan 27, 2005

### dextercioby

What "2"??Where did u pick it out???You mean the solution to the equation
$$\frac{\ln 4}{\ln x} =1$$

I hope you're only kidding...

Daniel.

9. Jan 27, 2005

### Erin_Sharpe

no, i'm kidding. this problem might as well be in chinese for all i understand of it

10. Jan 27, 2005

### Erin_Sharpe

*** NOT kidding

11. Jan 27, 2005

### dextercioby

Write it like that
$$\ln 4=\ln x$$

Use the fact that logaritm is a surjective function...

Daniel.

12. Jan 27, 2005

### Erin_Sharpe

i'm sorry i'm not trying to be difficult i just completely dont understand what you are talking about.

13. Jan 27, 2005

### dextercioby

Okay.Do you know the relation between the exponential and the natural logarithm???If so,apply exponential on both sides of the last equation and tell me what u get.

Daniel.