# The Logarithmic Function

Linear functions are useful in economic models because a solution can easily
be found. However non-linear functions can be transformed into linear
functions with the use of logarithms.

Given
the function

Taking
logarithms of both sides this function can be rewritten as

The resulting
function is linear in the log of the variables.

### An application of the logarithmic function

A production function describes the relation between output and the inputs
to a given process. A simple production function might relate output
to two inputs, labor and capital. (Capital typically includes plant and equipment.)
A production function might be used to study tradeoffs in the use of capital
and labor.

A well-known production function is the Cobb-Douglas Production function
which has the form

where

Q = the quantity of output

L = the quantity of labor

K = the quantity of capital

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