How Do You Estimate Logarithms Using Basic Logarithmic Properties?

[k3r0]

Homework Statement

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).

Homework Equations

log(ab)=log(a)+log(b)
log(a/b)=log(a)-log(b)
log(a^n)=nlog(a)

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).

 

[tiny-tim]

hi k3r0!

hint: log(125) ?

 

[Mark44]

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.

 

[k3r0]

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.

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

Thanks!

 

[TheoMcCloskey]

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

 

[Chestermiller]

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