how do you find this logarithim?

Question

log(sub 500)250

I really don't understand logarithms at all.

Explain??

Answer 1

Log Definition
The log of a number to a given base is the index of the power to which the base must be raised in order to give the number.

Examples
log base 10 (1000) = 3 because 10³ = 1000
log base 2 (16) = 4 because 2^4 = 16

In your question base is 500 and number is 250.
Let log be x
500^x = 250
x log 500 = log 250
x = log 250 / log 500 (where log can be to any base)

Sorry but I do not have access to a calculator at the moment. Hope you can follow explanation and obtain final answer.

Answer 2

Just need to convert the base (500) to another that is readily calculated. e.g. base 10 or base e can be easily evaluated using a calculator.
Using base 10, the base conversion is as follows:
log(base a) b = [log (base 10) b] / [log (base 10) a]
=> log(base 500) 250 = log(base 10) 250 / log(base10) 500
= 2.3979 / 2.6990
= 0.8885

Answer 3

log(sub 500)250 = x
we can rewrite this as 500^x = 250
from here we can take log to find x which would be answer to log(sub 500)250
500^x = 250
log(500^x) = log(250)
x*log(500)=log(250)
x=log(250)/log(500)
x=.88846486