Chapter 5.8, Problem 1AYU

To determine

Find the value of logarithm expression.

Answer to Problem 1AYU

  $\boxed{{\log }_{a}1=0}$

Explanation of Solution

Given information:

Find the value of logarithm expression.

  ${\log }_{a}1=$

Calculation:

Consider the logarithm function.

  ${\log }_{a}1=$

Apply the property of algorithm,

  ${\log }_{y}x=\frac{\log x}{\log y}$

  $\begin{array}{l}{\log }_{a}1=\frac{\log 1}{\log a}\\ \log 1=\log a^0\left[\therefore 1=a^0\right]\\ =0.\log a\\ =0\\ \sin ce\\ \log x^n=n\log x\\ {\log }_{a}1=\frac{0}{\log a}\\ \boxed{{\log }_{a}1=0}\end{array}$

Hence, $\boxed{{\log }_{a}1=0}$