What is the relationship between exponential and natural logarithm?

In summary, the given conversation is discussing the function y = logx 4 and its domain, range, and behavior. The function is defined for all values of x greater than 0 and has a range of all real numbers. Its derivative is positive for x < 1 and negative for x > 1, indicating that the function is increasing for x < 1 and decreasing for x > 1. The vertical asymptote is x = 0, the x-intercept is x = 1, and the value of x when y = 1 is approximately 1.1892. The function can also be rewritten as y(x) = ln 4 / ln x and its range is all real numbers. The relation between
  • #1
Erin_Sharpe
17
0
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!

thank you in advance!
 
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  • #2
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
So your function is:
[tex] y(x)=\log_{x} 4 [/tex]

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
I believe that loga(x) is only defined for a> 0. Does that help.
 
  • #5
Also I don't think that loga(x) is defined for a=1.
 
  • #6
Write
[tex] y(x)=\frac{\ln 4}{\ln x} [/tex]

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

Daniel.
 
  • #7
See I thought x was 2??
 
  • #8
What "2"??Where did u pick it out?You mean the solution to the equation
[tex] \frac{\ln 4}{\ln x} =1 [/tex]

I hope you're only kidding...

Daniel.
 
  • #9
no, I'm kidding. this problem might as well be in chinese for all i understand of it
 
  • #10
*** NOT kidding
 
  • #11
Write it like that
[tex]\ln 4=\ln x [/tex]

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

Daniel.
 
  • #12
i'm sorry I'm not trying to be difficult i just completely don't understand what you are talking about.
 
  • #13
Erin_Sharpe said:
i'm sorry I'm not trying to be difficult i just completely don't understand what you are talking about.

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.
 

FAQ: What is the relationship between exponential and natural logarithm?

What is a logarithmic function?

A logarithmic function is a mathematical function that is the inverse of an exponential function. It is expressed in the form y = logb(x), where b is the base of the logarithm. The logarithm of a number is the exponent to which the base must be raised to produce that number.

What is the difference between a logarithmic function and an exponential function?

The main difference between a logarithmic function and an exponential function is that the logarithmic function tells us what power we need to raise the base to in order to get a certain number, while the exponential function tells us what number we get when we raise the base to a certain power.

How do you graph a logarithmic function?

To graph a logarithmic function, we first need to determine the domain and range of the function. The domain is all positive real numbers and the range is all real numbers. Then, we plot points by choosing x-values and calculating the corresponding y-values using the logarithmic function. Finally, we connect the points to create the graph.

What are some real-life applications of logarithmic functions?

Logarithmic functions are used in a variety of fields, such as finance, biology, and acoustics. In finance, they are used to calculate compound interest and in biology, they are used to measure the pH level of a substance. In acoustics, they are used to measure the intensity of sound.

Can logarithmic functions have a negative base?

No, logarithmic functions cannot have a negative base. The base of a logarithm must be a positive number greater than 1. This is because a negative base would result in complex or imaginary solutions, which are not valid in logarithmic functions.

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