Chapter 4, Problem 36RE

To determine

To Evaluate: The Given Expression

  $2^{{\log }_{2}13}$

Answer to Problem 36RE

  $2^{{\log }_{2}13}=13$

Explanation of Solution

Given:To Evaluate the expression without using the calculator

  $2^{{\log }_{2}13}$

FORMULA USED:

  $\begin{array}{l}\text{properties of logarithms:}\\ a^{{\log }_{a}x}=x\end{array}$

Given: $2^{{\log }_{2}13}$

Using the property of the logarithms

  $\begin{array}{l}{a}^{{\log }_{a}x}=x\\ =2^{{\log }_{2}13}\\ =13\\ i.e\\ 2^{{\log }_{2}13}=13\end{array}$

Hence, $2^{{\log }_{2}13}=13$