CPM Homework Help : PC3 Problem 5-115

Given $\log_b(R)=5.4$ , $\log_b(Q)=1.2$ , and $\log_b(T)=−1.4$ , evaluate $\log_b\sqrt{\frac{RQ}{T}}$ .

Hint:

Break the expression up into three logarithms. Then substitute the given values.

Step 1:

$\text{log}_{b}\sqrt{\frac{RQ}{T}}=\text{log}_{b}\left(\frac{RQ}{T}\right)^{1/2}$

$=\frac{1}{2}\text{log}_{b}\left(\frac{RQ}{T}\right)$

$=\frac{1}{2}\left(\log_b(RQ)-\log_b(T)\right)$

$=\frac{1}{2}\left(\log_b(R)+\log_b(Q)-\log_b(T)\right)$