Combining several log terms

When adding and subtracting several log terms in the form $\log_{a} b$ , standard terminology would be ${log}_{b} (a)$ . 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)

= $\log_{6} (4 x 9)$ (Apply Log Rule 1)

= $\log_{6} 36$ (Simplify)

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

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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.