Chapter 8.4, Problem 20PPS

To determine

The solution of the equation in exponential form.

Answer to Problem 20PPS

  $d={10}^{\frac{w-65}{93}}$ .

Explanation of Solution

Given information:

The equation for wind speed $w,$ in miles per hour, near the centre of a tornado is $w=93{\log }_{10}d+65,$ where $d$ the distance in miles that the tornado travels is.

Calculation:

From the given information, the equation for wind speed $w,$ in miles per hour, near the centre of a tornado is $w=93{\log }_{10}d+65,$ where $d$ the distance in miles that the tornado travels.

  $\begin{array}{l}w-65=93{\log }_{10}d\text{ {Subtract 65 from each side}}\\ \frac{w-65}{93}={\log }_{10}d\text{ {Divide both sides by 93}}\\ d={10}^{\frac{w-65}{93}}\end{array}$

Thus, the solution is $d={10}^{\frac{w-65}{93}}$ .