Chapter EP, Problem 8.3.10EP

To determine

The value of logarithmic expression.

Explanation of Solution

Given information:

The given equation is ${\log }_{2}1024$

Calculations:

To convert the logarithmic function into exponential function, we should know the concept below.

Let $b$ and $x$ be positive numbers with $b\ne 0$ . The logarithm of x with base b is denoted is denoted by ${\log }_{b}x$ and is defined as exponent $y$ that makes the equation $b^y=x$ true.

Following the rule we can convert the equation in exponential form. Then we can find the value of the expression.

  $\begin{array}{l}{\log }_{2}1024=y\\ 2^y=1024\\ 2^y=2^{10}\\ \text{comparing both sides we can write,}\\ y=10\\ Thus,\\ {\log }_{2}1024=10\end{array}$