Hi,

I was working through a log problem using logarithmic identities. The problem is worded as follows:

log(4) = 0.703x

log(1/4) = z

solve for z in terms of x

To solve this, I tried one approach, which is simply:

z = log(1/4) = log(4^-1) = -1*log(4) = -0.703x.

This seems to be the correct answer. Then I also tried solving the same question by adding the two equations together:

log(4) + log(1/4) = 0.703x + z

so:. The solution in this case is also in agreement.z = log(4*(1/4)) - 0.703x = -0.703x

My question is... why does it not work when you subtract one equation from the other? My work comes out like this:

log(4) - log(1/4) =0.703x - z

The z in this case doesn't agree with z in the other cases. Can anyone tell me what I am doing wrong in the last case? Thanks.log[4/[1/4]] = .703x - z

log(16) = .703x - z

z = .703x - log(16)