# Reducing non-linear laws to a linear form?

Reduce the following non-linear relation between x and y to the linear form Y = mX + c, given that a and b are constants

y^3 = a x (x^k)

Here's what I did:

3 log y = log ax^k

..........= log a + log x^k

..........= k log x + log a

m = k,

c = log a ,

y-axis is 3 lg 3, and x-axis is lg x

If it's wrong can someone explain to me why? Thanks

Correction for my working: y-axis is 3 log y.

### 1 Answer

- SqdancefanLv 72 years agoFavorite Answer
Seems basically correct, assuming the first "x" in your a x (x^k) is supposed to be a multiplication symbol, not a variable. You could divide through by 3 to have

.. log(y) = (k/3)*log(x) +log(a)/3

.. Y = log(y)

.. m = k/3

.. X = log(x)

.. c = log(a)/3

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We usually use an asterisk (*) or raised dot (• or ·) or actual multiplication symbol (×) if a multiplication symbol is needed. (Be aware there are a couple of posters on here who use a raised dot for a decimal point and a period for a multiplication symbol: 6.2•3 = 13•8 in those terms, where most of us would interpret that as 18.6.)

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