All explanatory variables except initial income are country averages for the 1980-2000 period; all are entered as

natural logarithms.

Finally, we ran a regression of the rate of change of the

natural logarithm of the inflation-adjusted average hourly earnings (i.

For each year I took the

natural logarithms of the following variables:

In minimising the AIC and SBC, we minimise the

natural logarithm of the residual sum of squares adjusted for sample size, T, and the number of parameters included, n.

The equation used in the regression analysis is the

natural logarithm of equation 1.

t] where [alpha] [less than to] 0, and [mu] is the aggregate supply shock proxied by the change in the

natural logarithm of the relative price of crude oil; [mu] is measured by the difference of the first difference of the

natural logarithms of the nominal price of Saudi crude oil and the implicit price deflator.

Application of the series expansion for

natural logarithms to (5), followed by application of the generalized jackknife to the resulting bias expansion, allows us to write (11) as follows:

Set in a fairy tale land, the illustrated stories in this supplement textbook demonstrate the concepts behind the slope of a tangent line, derivatives, integrals,

natural logarithms, exponential functions, integration, differential equations, partial derivatives, and numerical methods.

For a given number, the idea is to find

natural logarithms repeatedly until the result lies between 1 and 0.

Someone once proposed naming the unit of

natural logarithms (e = 2.

Thus, our empirical specifications include the

natural logarithm of REER to capture the influence of relative prices.