I'm going to simulate oil price shocks and see what effect they have
on the swedish unemployment. I have estimated the following function:
Y = -102,75 + 21,15 * X
where Y is the unemployment and X is the oil price. My supervisor want
me to change this model to a log-log model using the natural logarithm
instead. How do I do that in Excel?

Hello bylla!
I understand here that, instead of estimating a linear model (like the
one you describe above), your supervisor wants you to estimate the
following log-log model:

log(Y) = A + B*LOG(X)

which, by taking e to the power of the left and right-hand side of
this equation, becomes:

Y = (e^A) * e^(B*LOG(X))
  =   D   * (e^LOG(X))^B
  =   D * X^B

where D=e^A is the constant term (the equivalent to your -102.75 in
the log-log model)

It's very easy to do this en Excel. First of all, you need to create
two new columns, one being the natural logarithm of Y and the other
one being the natural log of X. This is done by using the command LN
in Excel. For example, if you have Y in column A and X in column B,
you should put, say, in cell C1:

=LN(A1)

and then copy this command to each row in column C. This will generate
a column that will be log(Y). Doing the same in the next column
generates log(X).

Once you have these new columns created, just use the same command you
used in order to obtain the estimated function you show in your
question (you may have done this by using the TREND command, or by
using the Regression in the Data Analysis Toolpack) on the NEW
columns. The coefficients you obtain will be the ones of the log-log
model. That is, you will get an A and B that will estimate the
function:

log(Y) = A + B*log(X)

As I've shown above, these corresponds to a model where:

Y = (e^A) * (X^B)


I hope this was clear enough. If you have any doubts regarding my
answer, please request a clarification before rating it.

Best wishes!
elmarto