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

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SUMMARY

The equation log(x) = ln(x)/ln(10) is validated through the change of base formula, which states that log_a(b) = log_c(b)/log_c(a). This formula allows for the conversion of logarithmic bases, confirming that the logarithm of x in base 10 can be expressed in terms of the natural logarithm. Participants in the discussion emphasized the importance of understanding this formula for proving logarithmic identities without numerical examples.

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