# Showing that the least-square method minimizes error

Assume that the relation between temperature and time is defined as follows: $$T = A^kC$$ We can find parameters $A$ and $C$ using the least-square method. The given relation is not linear, but we can circumvent this problem using the following relation between $log(T)$ and $k$: $$log(T) = k log(A) + log(C)$$ How can I show that because of this transformation, the least-square method, bij approach, minimizes the sum of the squares of relative temperature errors (given that these are small enough)?

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