How can log(x) = ln(x)/ln(10)?

  • B
  • Thread starter Natalinatul
  • Start date
In summary, the conversation discusses a method for proving an equation without using numbers and the concept of changing bases in logarithmic equations. The conversation also includes a correction and clarification about the change of base formula.
  • #1
Natalinatul
5
1
Might be a silly question but I'm trying to search for ways to prove that it's right without using the numbers itself
 
Mathematics news on Phys.org
  • #2
Natalinatul said:
Might be a silly question but I'm trying to search for ways to prove that it's right without using the numbers itself
Does the following equation make sense to you:
$$x=10^{log x}$$
It says that, by definition, the log of x is the power to which you have to raise 10 to get x.
 
  • Like
Likes Natalinatul
  • #3
Chestermiller's answer is correct, and so by this time you may have figured this out, but if you are still having difficulty, just google the proof of the change of base formula. Or just google the change of base formula, and many sites will also offer the proof (based on Chestermiller's hint)
 
  • Like
Likes Natalinatul
  • #4
Yup.. How could I miss that! The best thing about his answer was the fact he didn't answer it but gave a great hint... I figured it out now...
 
  • Like
Likes DrewD
  • #5
Hi, there is this formula ##\log_{a}{b}=\frac{\log_{c}{b}}{\log_{c}{a}}## that permits to change the base from ##b## to ##c##.
 
  • #6
Ssnow said:
Hi, there is this formula ##\log_{a}{b}=\frac{\log_{c}{b}}{\log_{c}{a}}## that permits to change the base from ##b## to ##c##.
Don't you mean when you change the base from c to a?
 
  • Like
Likes symbolipoint and nomadreid
  • #7

FAQ: How can log(x) = ln(x)/ln(10)?

What is the relationship between log(x) and ln(x)?

The logarithm function and the natural logarithm function are closely related. The logarithm function, log(x), is the inverse of the exponential function, while the natural logarithm function, ln(x), is the inverse of the natural exponential function. In other words, log(x) and ln(x) are inverse functions of each other.

Why is ln(x)/ln(10) used to represent log(x)?

The base 10 logarithm, log(x), can be written as log(x) = ln(x)/ln(10). This is because the logarithm function with any base, b, can be rewritten as the natural logarithm function with base e (ln) divided by the natural logarithm of that base (ln(b)). So, ln(x)/ln(10) is just a way to represent log(x) using the natural logarithm function.

How do you convert from log(x) to ln(x)?

To convert from log(x) to ln(x), use the formula ln(x) = log(x)/log(e), where log(e) is equivalent to ln(10). So, to convert a log with base 10 to a natural logarithm, divide the log by ln(10).

Is there a difference between log(x) and ln(x)?

Yes, there is a difference between log(x) and ln(x). Log(x) is the logarithm function with base 10, while ln(x) is the natural logarithm function with base e. The natural logarithm function is often used in mathematical and scientific calculations, while the logarithm function with base 10 is commonly used in everyday calculations.

Why is log(x) commonly used in science and engineering?

Log(x) is commonly used in science and engineering because it simplifies calculations involving large numbers. For example, the Richter scale used to measure earthquakes is based on log(x), which allows for a wider range of magnitudes to be represented on a linear scale. Additionally, log functions are useful in analyzing data that follows exponential patterns, such as population growth or radioactive decay.

Similar threads

Replies
44
Views
4K
Replies
13
Views
1K
Replies
6
Views
4K
Replies
4
Views
2K
Replies
6
Views
2K
Back
Top