Chapter 3.3, Problem 28E

Solution

To evaluate: the given logarithmic expression if it is defined using a calculator, and check your result by evaluating the corresponding exponential expression.

Undefined

Given information:

The expression:

  $\log \left(-5.14\right)$

Definition Used:

Common logarithm- Base 10:

The common logarithmic function ${\log }_{10}x=\log x$ is the inverse of the exponential function $f\left(x\right)={10}^x$ . Therefore,

  $y=\log x$ if and only if ${10}^y=x$

Explanation:

The value of $\log \left(-5.14\right)$ is not defined, as logarithm is not defined for negative numbers.

Inputting $\log \left(-5.14\right)$

in the calculator gives the following error message:

  

It can also be verified as:

By the above definition of common logarithm:

  $y=\log x$ if and only if ${10}^y=x$

But there exists no real number y such that ${10}^y=-5.14$ .

Hence, value is undefined.