### Home > PC3 > Chapter 5 > Lesson 5.2.5 > Problem5-115

5-115.

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

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

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

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

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

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