The variables $x$ and $y$ are related by the equation $y=a{{b}^{x}}-3$. When \(\lg \left(

Question

The variables $x$ and $y$ are related by the equation $y=a{{b}^{x}}-3$. When $\lg \left( y+3 \right)$ is plotted against $x$, a straight line graph is obtained which passes through $\left( -2,5 \right)$ and $\left( 10,-1 \right)$. Find the value of $a$ and $b$.

Accepted Answer

$a = 10^4 = 10000\; \quad b = 10^{-\frac{1}{2}} = \frac{1}{\sqrt{10}}$

Linear Law - Linearisation Using Logarithms

Linear Law - Linearisation Using Logarithms

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