what is equal to log(8)15 + log(8)25- log(8)3?

Question

the numbers in the parenthesis are suppose to be the small number the goes next to the g in log.

Answer 1

Okay, you have a bunch of base-8 logs of numbers.  This is a question to make sure you understand what logs are.  

 

log8(X), called "log to the base 8 of X), is the number that, if 8 is multipied by itself that many times, will result in the number X.  For example, if X is 64, then log8(X) is 2.  If X is 16, then log8(X) is 4/3.  If X is 4, then log8(X) is 2/3.  If X is 2, log8(X) is 1/3.

 

Now, if I add two logs, log8(X) and log8(Y), then I get the number that is the log of the product of X and Y... log8(XY).

 

You can test this with the sample numbers I just gave you up there.  If you add 4/3 (the log8 of 16) and 2/3 (the log8 of 4), then you get 2 (the log8 of 64, which is 16*4).

 

This is because of what a log is - the number of times you have to multiply the base (8) together in order to get the number.  

 

Also, if you subtract the log of some Z, that's taking the log of something that was divided by Z.  The reasoning is the same - you're taking away that many factors of the base (8) from the product.

 

 

So, log8(15) + log8(25) = log8(15*25)

 

And log8(25) - log8(3) = log8(25/3)

 

So, given this discussion, can you finish the problem?

 

 

 

Answer 2

I assume these are log base 8. So, first use the log product and quotient rule to combine the terms:

 

log(a+b-c)= log(a*b/c)

 

so you should get log(8)125.

 

Then find out, '8' to the what = 125.

 

- Ben