Refresher - Combining Several Log Terms

Combining several log terms

When adding and subtracting several log terms in the form ${\log }_{a}b$, standard terminology would be ${\displaystyle {log}_b\left(a\right)}$. There is a simple way to combine all the terms in one step. Remember that all the logs must have the same base.,
• Multiply the arguments of the positive log terms in the numerator,
• Multiply the arguments of the negative log terms in the denominator.

= log⁡ 6 4+2 log⁡ 6 3

= ${\log }_{6}4+{\log }_6{3}^2$ (Apply Log Rule 3)

= ${\log }_{6}4+{\log }_{6}9$ (Simplify the exponent)

= ${\log }_6(4x9)$ (Apply Log Rule 1)

= ${\log }_{6}36$ (Simplify)

= 2 (Since $6^2=36$)

 

 

 

 

 

 

 

Math 1A/1B: Pre-Calculus by Dr. Sarah Eichorn and Dr. Rachel Lehman is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License Links to an external site..