Quick question about logarithm...

[JonTheBaller]

How do I prove

log sub-c (ab) = log sub-c (a) + log sub-c (b)?

Thanks.

 

[Jmmsbnd007]

With a proving machine.

 

[her209]

By induction.

 

[JonTheBaller]

Thanks, just didn't know how to begin (going to use induction).

 

[Haircut]

I don't see why you would use induction to solve this.

All you need to do is represent a and b as powers of c and calculate the logs in base c.

 

[JonTheBaller]

Originally posted by: Haircut
I don't see why you would use induction to solve this.

All you need to do is represent a and b as powers of c and calculate the logs in base c.

Can you explain further?

 

[gopunk]

Originally posted by: johnnytightlips
How do I prove

log sub-c (ab) = log sub-c (a) + log sub-c (b)?

Thanks.

c^(logsub-c(a) + logsub-c(b) = ab
c^logsub-c(ab) = ab
ab = ab


given to first is by def.
first to second is just a property of log.... it's in your textbook probably
2nd to third is by def. of log,

 

[Haircut]

What you would do is let a = c^x, b = c^y
Now, ab = c^x * c^y = c^(x+y)

Now just take logs of a, b and ab.

 

[her209]

assume a=b=c

then:

logc (a) = 1
logc (b) = 1
logc (a*b) = 1 + 1 = 2