Chapter 4.6, Problem 10P

Solution

To explain: How to find the equation’s accurate solution using the table.

Given:

An equation $4^x=11$.

Concept used:

1. To obtain obtain the solution using a table, look for the value of $x$ for which the function produces the value which is closer to the original equation value.

Explanation:

Consider that both sides of the equation represent a function. So, it can be assumed that $y=4^x$ and $y=11$ . Now find the value of $y=4^x$ at different values of $x$.

$x$	$y$
$1.5$	$8$
$1.6$	$9.19$
$1.7$	$10.556$
$1.71$	$10.703$
$1.72$	$10.853$
$1.73$	$11.004$

From the table data, it can be understood that the precise solution can be obtained by substituting such values of $x$ in the function for which the $y$ value is very much closer to the original exponential equation value.

Here, in this problem. For $x=1.73$ the value of $y$ is $11.004$ which is very much closer to the original equation value that is $11$ . So, $x=1.73$ is very accurate solution of this problem.

Conclusion:

The precise solution can be obtained by substituting such values of $x$ in the function for which the $y$ value is very much closer to the original exponential equation value.