Thread: a basic logarithmic inquiry...

hello--

It is understood that a logarithmic notation:



That is certainly straight forward. But, please clarify: how to correlate the above expression with the following:


10 log 2 = 3

10 log 10 = 10

10 log 1,000,000 = 60

Even entering a calculator elicits the above, but I am unable to relate "10 log 1000000 = 60" to (merely as an example) "log 2 (8) = 3"

I can do the math for "log 2 (8) = 3" (I am multiplying 2 by itself 3 times to produce 8) but I cannot explain how (again, only as an example) "10 log 1,000,000 = 60"


I hesitate to pose this inquiry only because I feel certain the explanation will appear quite obvious...

thank you!

Calculators usually do base 10 logs.

log rules say

so 10 log 10 or
same applies for all the other expression you provided.

basically ask your self, base b raised to what power gives the expression inside the log.

(2 raised to what power gives me ? 3, so

Originally Posted by stonewhite

hello--

It is understood that a logarithmic notation:



That is certainly straight forward. But, please clarify: how to correlate the above expression with the following:


10 log 2 = 3

10 log 10 = 10

10 log 1,000,000 = 60

Even entering a calculator elicits the above, but I am unable to relate "10 log 1000000 = 60" to (merely as an example) "log 2 (8) = 3"

I can do the math for "log 2 (8) = 3" (I am multiplying 2 by itself 3 times to produce 8) but I cannot explain how (again, only as an example) "10 log 1,000,000 = 60"


I hesitate to pose this inquiry only because I feel certain the explanation will appear quite obvious...

thank you!

All the logarithms you mentioned above use (nearly!) the base 10.



and



Only



is a very roughly rounded value.

thank you both!