Chapter 8.6, Problem 68HP

To determine

To find: Sam and Rosamaria are solving $4^{3p}=10$ whether of the correct is.

Answer to Problem 68HP

The Sam’s reasoning is incorrect and Rosamaria’s is correct.

Explanation of Solution

Given information:

The given solutions by Sam and Rosamaria,

  

Calculation:

Consider the problem;

  $4^{3p}=10$

Consider the Sam’s reasoning,

  $\begin{array}{c}{4}^{3p}=10\\ \log 4^{3p}=\log 10\\ p\log 4=\log 10\\ p=\frac{\log 10}{\log 4}\end{array}$

Unfortunately Sam made mistake on th third line as the correct statement is,

  $3p\log 4=\log 10$

Thus,

  $p=\frac{1}{3}\frac{\log 10}{\log 4}$

Therefore, the Sam’s reasoning is incorrect and Rosamaria’s is correct.