What Is the Error of Log(mh) When m and h Have Known Relative Errors?

[excel000]

Homework Statement

If the relative error of m is 1% and of h is .5%, what is the error of log(mh)?

Homework Equations

d/dx(lnx)=1/x, \deltalnx=\deltax/x

The Attempt at a Solution

\delta(ln0.43(mh))=\delta(0.43lnm + 0.43lnh)
=\delta(0.43ln0.01 + 0.43ln0.005)
=-4.26

i'm pretty sure this isn't right since it's a negative number, i have no idea how to do this

 

[Redbelly98]

I don't see how the 0.43 is coming into this.

First, what's the relative error in m*h?

Second, if you want the error in ln(x), replace x with x₀(1±ε). (ε is the relative error in x).

See if you can work it from there.