Chapter 3.3, Problem 91E

To determine

To find: The logarithmic equation that relates given $y$ and $x$ .

Answer to Problem 91E

  $\ln y=-0.1734\ln x$ .

Explanation of Solution

Given information:

A table of values is given as −

  

Calculation:

A table of values is given as −

  

Step $1$ : Taking natural logarithm of both $x\text{ and }y$ .

$\ln x$	$0$	$0.693$	$1.0986$	$1.3863$	$1.6094$	$1.7917$
$\ln y$	$0.9163$	$0.7429$	$0.6418$	$0.5698$	$0.5140$	$0.4681$

Step $2$ : Plot these points on a coordinate axes.

  

All points are in straight line.

Step $3$ : Take any two points to determine slope of the line.

  $m=\frac{0.7429-0.9163}{0.693-0}=-0.1734$

Step $4$ : Using point slope formula, equation of the line would be -

  $\begin{array}{l}Y=mX\\ \Rightarrow Y=-0.1734X\text{ ;where }Y=\ln y,X=\ln x\\ \Rightarrow \ln y=-0.1734\ln x\end{array}$

Hence, desired logarithmic equation is $\ln y=-0.1734\ln x$ .