# Thread: Change-of-Base Formula

1. ## Change-of-Base Formula

Use the change-of-base formula and a calculator to evaluate each logarithm.

(1) log_5 (18)

(2) log_π (sqrt{2})

Note: The symbol π stands for pi.

2. the change of base formula is usually used to change to log base 10 or log base e because those are the log keys available on most calculators.

to change from base "b" to base 10 or base e ...

$\displaystyle \log_b(x) = \frac{\log(x)}{\log(b)} = \frac{\ln(x)}{\ln(b)}$

get out your calculator and try it.

3. ## Are you...

In the questions given, b represents base 5 and pi and x represents 18 and sqrt{2}. Is this what you are saying?

Are you also saying that log(x)/log(b) is the same as written ln(x)/ln(b)?

Then I just plug and chug, right?

Should I then round off the answers to the second or third decimal places? Which one?

4. Originally Posted by magentarita
In the questions given, b represents base 5 and pi and x represents 18 and sqrt{2}. Is this what you are saying? Mr F says: In your question 1, b = 5 and x = 18. In your question 2, b = n and x = sqrt{2}. I don't know where you have got pi from.

Are you also saying that log(x)/log(b) is the same as written ln(x)/ln(b)? Mr F says: Yes s/he is.

Then I just plug and chug, right? Mr F says: Yes.

Should I then round off the answers to the second or third decimal places? Which one? Mr F says: Impossible to answer. The original question should state what accuracy is required.
In fact, $\displaystyle \log_b(x) = \frac{\log_a (x)}{\log_a (b)}$for any base a > 0 and $\displaystyle a \neq 1$.
Skeeter stated the formula for when you change to base 10 or base e - this is because you have to calculate a numerical value and even a scientific calculator has a log base 10 and log base e button.

5. ## There is pi...

This is the exact question 2 as given in the textbook:

log_pi (sqrt{2})

How do you solve that when there is pi in the question itself?

6. $\displaystyle \pi$ is just a number ... treat it as you would any other constant.

Thanks