Chapter EP, Problem 8.7.22EP

To determine

To find: The equation or inequality and round to the nearest ten thousandth.

Answer to Problem 8.7.22EP

The equation or inequality and round to the nearest ten thousandth $x=52.5982$ .

Explanation of Solution

Given information:

The given equation is $(x+2)=4$ .

Calculation:

Consider $b$ and $x$ be positive numbers $b\ne 1$ . The logarithm of $x$ with base b is denoted by ${\log }_{b}x$ and is defined as the exponent y that makes the equation $b^y=x$ true.

Consider the following properties of logarithms,

Calculate the logarithm.

${\log }_b\frac{m}{n}={\log }_{b}m-{\log }_{b}n$

Product properly:

${\log }_{b}mn={\log }_{b}m+{\log }_{b}n$

Power property:

${\log }_b{m}^p=p{\log }_{b}m$

Consider the following equation:

In $(x+2)=4$

Write each side using exponents and base $e$

$e^{In(x+2)}=e^4$

Apply inverse property of exponents and logarithm:

$x+2=e^4$

Subtract 2 from both sides:

$x=e^4-2$

Use Ti-83 calculator to solve above value:

Therefore, the equation or inequality and round to the nearest ten thousandth $x=52.5982$ .