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 $c$. $\sqrt{y} = \frac{p}{\sqrt{yx}} - \frac{b}{x}$ $y = b^{2x} - 1$ $y = ac^x - x$

Accepted Answer

(a) $Y=x\sqrt{y}$, $\displaystyle X=\frac{x}{\sqrt{yx}}$, $m=p$, $c=-b$ (b) $Y=\ln(y+1)$, $X=x$, $m=2\ln b$, $c=0$ (c) $Y=\ln(y+x)$, $X=x$, $m=\ln c$, $c=\ln a$

Linear Law - Linearisation Using Logarithms

Linear Law - Linearisation Using Logarithms

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