Chapter 11.5, Problem 1CFU

To determine

To demonstrate: The fact that $\log 1=0$ and $\log 10=1$ .

Answer to Problem 1CFU

The fact used is ${10}^y=x$ .

Explanation of Solution

Given:

The given fact is $\log 1=0$ and $\log 10=1$ .

Calculation:

The common logarithms of numbers that differ by integral power of ten are closely related. In the equation $y=\log x$ , $y$ is the power to which $10$ is raised to obtain the value of $x$ .

The result of the equation $y=\log x$ is ${10}^y=x$ . Therefore, $\log 1=0$ because ${10}^0=1$ , and $\log 10=1$ because ${10}^1=10$ .

Therefore, the fact used is ${10}^y=x$ .