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

Might be a silly question but I'm trying to search for ways to prove that it's right without using the numbers itself

Chestermiller
Mentor
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.

Natalinatul
Gold Member
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)

Natalinatul
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...

DrewD
Ssnow
Gold Member
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##.

Chestermiller
Mentor
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?