Chapter EP, Problem 8.6.19EP

To determine

To find: The logarithm in terms of common logarithms and its value to four decimal places.

Answer to Problem 8.6.19EP

The logarithm in terms of common logarithms and its value to four decimal places is ${\log }_{3}21=2.7712$ .

Explanation of Solution

Given information:

The given expression is ${\log }_{3}21$ .

Calculation:

Consider the following expression.

${\log }_{3}21$

Let 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.

For all positive numbers $a$ , $b$ and $n$ where $a\ne 1$ and $b\ne 1$ .

${\log }_{a}n=\frac{{\log }_{b}n}{{\log }_{b}a}$

Now evaluate the expression ${\log }_{3}21$ :

${\log }_{3}21=\frac{{\log }_{10}21}{{\log }_{10}3}$

Use calculator to evaluate the expression.

Therefore, the logarithm in terms of common logarithms and its value to four decimal places is ${\log }_{3}21=2.7712$ .