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{yx}=\frac{𝑎}{\sqrt{𝑦}}−\frac{𝑏}{𝑦}$
$y = a^{3x} - 4$
$xy = ac^x + 2x$

Accepted Answer

(a) $Y=y\sqrt{x}$, $X=\dfrac{1}{\sqrt y}$, $m=-b$, intercept $a$; (b) $Y=\ln(y+4)$, $X=x$, $m=3\ln a$; (c) $Y=\ln[x(y-2)]$, $X=x$, $m=\ln c$, intercept $\ln a$.

Linear Law - Linearisation Using Logarithms

Linear Law - Linearisation Using Logarithms

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