Chapter 8.3, Problem 12CYU

To determine

To Write: The equation in exponential form of the inverse of the function.

Answer to Problem 12CYU

  $PS={10}^R$

Explanation of Solution

Given: Use the information at the beginning of the lesson. The Palermo scale value of any object can be found using the equation $PS={\log }_{10}R$ where $R$ the relative risk posed by the object.

Given: $PS={\log }_{10}R$

  $\begin{array}{l}{\log }_{b}x=yifandonlyif\\ b^y=x\end{array}$

Then equation in exponential form

  $\begin{array}{l}PS={\log }_{10}R\\ {10}^{PS}=R\end{array}$

Thus

  $R={10}^{PS}$

Now flip the equation to find the inverse of the equation

We get

  $PS={10}^R$

Hence, $PS={10}^R$