Convert each of the following non-linear equations, where $a$, $b$ and $c$ are constants,

Question

Convert each of the following non-linear equations, where $a$, $b$ and $c$ are constants, into the linear form $Y = mX + c$. State the variables of $Y$ and $X$ in terms of $x$ and/or $y$. Also, the constants $m$ and $c$ in terms of $a$, $b$ and $c$.

$y = \frac{a}{x^2} - bx$
$y = a^x - 4$
$\frac{2}{y} = ax^2 - \frac{b}{x}$

Accepted Answer

(a) e.g. $Y=\frac{y}{x},X=\frac{1}{x^3}$ or $Y=yx^2,X=x^3$. (b) $Y=\lg(y+4),X=x,m=\lg a,c=0$. (c) e.g. $Y=\frac{x}{y},X=x^3$, $m=\frac{a}{2},c=-\frac{b}{2}$.

Linear Law - Linearisation Using Logarithms

Linear Law - Linearisation Using Logarithms

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