# Homework Help: Estimate the values of log(4)

1. Dec 5, 2013

### k3r0

1. The problem statement, all variables and given/known data
Given that log(2) is roughly 0.30 and log(∏) is roughly 0.5, estimate the values of log(4), log(5), log(6) and log(8).

2. Relevant equations
log(ab)=log(a)+log(b)
log(a/b)=log(a)-log(b)
log(a^n)=nlog(a)

3. The attempt at a solution
I found log(4) and log(8) using log(2)+log(2) [+log(2)], and i estimated log(6) using log(2)+log(∏), but i don't know how to get to log(5).

2. Dec 5, 2013

### tiny-tim

hi k3r0!

hint: log(125) ?

3. Dec 5, 2013

### Staff: Mentor

My guess, assuming there isn't a mistake in the problem statement, is that they want you to use linear interpolation. log(5) ≈ (1/2)(log(4) + log(6)). This would be the average (or mean) of the two log values.

4. Dec 5, 2013

### k3r0

Thanks a lot, that method never crossed my mind. I spent about half an hour being irritated at that question, haha.

Thanks!

5. Dec 6, 2013

### TheoMcCloskey

another hint: what is $\pi^2$ equal to?

6. Dec 7, 2013

### Staff: Mentor

log(5)=log(10)-log(2) = 1 - log(2) = 0.7