Chapter EP, Problem 8.7.24EP

To determine

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

Answer to Problem 8.7.24EP

The equation or inequality and round to the nearest ten thousandth is $49.8044$ .

Explanation of Solution

Given information:

The given equation is $(3x-1)=5$ .

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 $(3x-1)=5$

Write each side using exponents and base e:

$e^{In(3x-1)}=e^5$

Apply inverse property of exponents and logarithm:

$3x-1=e^5$

Add 1 to both sides:

$3x=e^5+1$

Divide both sides by 3:

$x=\frac{e^5+1}{3}$

Use Ti-83 calculator to solve above value:

Therefore, the equation or inequality and round to the nearest ten thousandth is $49.8044$ .