Checkpoint: Approximate Logarithms with Technology Solution

Write $\log 63$ in terms of P and Q when $\log 3 = P$ and $\log 7 = Q$ .
Calculate the approximate value of $\log 63$ when $\log 3 \approx 0.4771$ and $\log 7 \approx 0.8451$ .

$\begin{array}{rcl} \log 63 & = & \log (3^{2} \cdot 7) \\ = & \log 3^{2} + \log 7 \\ = & 2 \log 3 + \log 7 \\ = & 2 (P) + (Q) \\ = & 2 P + Q \\ \approx & 2 (0.4771) + (0.8451) \\ \approx & 1.7993 \end{array}$

2P+Q  
1.7993

Note

Make sure both parts of the problem are completed. Part A ensures the rules of logs are used before technology is utilized.

Q: What rules did you use to expand the argument?

A: The power and the product rules.