Logarithms conversion help

[bardothello]

Hi,

going by the formula

$$c = log(base, x)(b) / log(base, x)(a) = log(base, a)(b)$$,

I think that I can have any x value, and that this doesn't just work for x=10 correct?
Every example i see people choose x=10 I think because it simplifies things, but I want to make sure that any x value would work.

Also, can someone tell me how to type a (base) with this format? And did I do the dividing sign wrong, or is that how it is supposed to look?

Thanks in advance!

 

[MarkFL]

Yes, the base change formula will allow you to change from any valid base to another. As far as the $\LaTeX$ goes, this code:

\frac{\log_a(b)}{\log_a(c)}=\log_c(b)

placed within appropriate tags, produces:

[MATH]\frac{\log_a(b)}{\log_a(c)}=\log_c(b)[/MATH]

 

[bardothello]

Great! Thanks a lot

 

[Deleted member 4993]

Hi,

going by the formula

$$c = log(base, x)(b) / log(base, x)(a) = log(base, a)(b)$$,

I think that I can have any x value, and that this doesn't just work for x=10 correct?
Every example i see people choose x=10 I think because it simplifies things, but I want to make sure that any x value would work.

Also, can someone tell me how to type a (base) with this format? And did I do the dividing sign wrong, or is that how it is supposed to look?

Thanks in advance!

As long as x>= 0 (non-zero positive number)

 

[lookagain]

As long as x>= 0 (non-zero positive number)

x > 0

Regarding your parenthetical phrase, a positive number already is non-zero.

Also, not only is x greater than 0, it cannot equal 1.

 

[Deleted member 4993]

x > 0

Regarding your parenthetical phrase, a positive number already is non-zero.

Also, not only is x greater than 0, it cannot equal 1.

Correct ... I was hoping OP will comment on that and then I could extend my statement and explain why. But......

 

[lookagain]

Correct ... I was hoping OP will comment on that and then I could extend my statement and explain why. But......

"But?" No, I disagree with your take that I gave away an additional learning experience.
I took it as I was going in as fast as possible to A) clear up an inconsistent/self-contradictory
post of yours and B) to not let the OP think what you stated was sufficient (sin of
omission) by not stating an extra condition.

 

[JeffM]

Subhotosh

You have SINNED. What a naughty man!

 

[Otis]

… Every example i see people choose x=10 I think because it simplifies things …

Yes, it simplifies introductory lessons on logarithms. Also, calculators have a base-10 button for logs, so that base is common in class. The change-of-base formula is very handy when we need to evaluate a logarithm whose base is different than 10 (because, after changing to base 10, we can use a calculator).

If you're familiar with the base-e logarithm, then you probably know that calculators have a button for that, also. What you might not yet know is a word of caution about 'log' notations that don't display a base.

In math classes (initially), the expression log(x) stands for log₁₀(x), and ln(x) stands for the natural logarithm log_e(x).

However, someday you may encounter materials where log(x) represents log_e(x) or log₂(x) because some authors prefer using the name 'log' to represent the base most common in their field (eg: math professors may use base-e almost exclusively, while computer scientists mostly use base-2). Hopefully, the context lets us know what log(x) means or we have given values enabling us to confirm the base. Otherwise, we need to ask.

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