## Precalculus (6th Edition) Blitzer

The number of miles is $5.5\text{ miles}$.
As per the question, $P\left( x \right)=14.7{{e}^{-0.21x}}$ Substitute the values of $P\left( x \right)$ in the above equation and simplify: $4.6=14.7{{e}^{-0.21x}}$ And divide both sides of the equation by $14.7$ and simplify as follows: \begin{align} & \frac{4.6}{14.7}=\frac{14.7}{14.7}{{e}^{-0.21x}} \\ & 0.31={{e}^{-0.21x}} \end{align} Write the above exponential form in logarithmic form using: If ${{b}^{y}}=x$, then ${{\log }_{b}}x=y$ So, $0.31={{e}^{-0.21x}}$ is equivalent to ${{\log }_{e}}0.31=-0.21x$. Solving the above expression as follows: \begin{align} & {{\log }_{e}}0.31=-0.21x \\ & -1.17=-0.21x \end{align} Change the sides of the equation and divide both sides by $-0.21$, \begin{align} & \left( \frac{-0.21}{-0.21} \right)x=\frac{-1.17}{-0.21} \\ & x=5.5 \end{align} Thus, the peak of Mt. Everest is $5.5\text{ miles}$ above sea level.