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 $c$. $y = ax^2 - \frac{b}{x}$ $y = 2 + b^x$ $\frac{1}{y} = ax^3 - \frac{b}{x^2}$

Accepted Answer

(a) $Y=xy$, $X=x^3$, $m=a$, $c=-b$ (b) $Y=\ln(y-2)$, $X=x$, $m=\ln b$, $c=0$ (c) $\displaystyle Y=\frac{x^2}{y}$, $X=x^5$, $m=a$, $c=-b$

Linear Law - Linearisation Using Logarithms

Linear Law - Linearisation Using Logarithms

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