Advanced Math/Logarithms

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Expert: Sherry Wallin - 12/13/2010


Question
Hello Ms.Sherry!
   I have this question,in which I am not able to move forward.Can you tell me what should I do next:
1/2 log_3 144 - log_3 4 + 2log_3 3
= 1/2 log_3 (144/4) + 2log_3 3(acc to quotient law)
= 1/2 log_3 (36) + 2log_3 3
I could have used the product law but there is 1/2 and 2 stopping me! Can you please tell me what should I do?
                               Thankyou!

Answer
Xiang~

This is what I would do:
(1/2)log_3(144) - log_3(4) + 2log_3(3)
= (1/2)log_3(12^2)-log_3(4) + log_3(3^2)
= log_3(12^2)^(1/2) -log_3(4) + 2
= log_3(12) - log_3(4) + 2
= log_3(4*3) - log_3(4) + 2
= log_3(4) + log_3(3) - log_3(4) + 2
= 1 + 2
= 3

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Sherry Wallin

Expertise

I can answer most questions up through Calculus and some in Number Theory and Abstract Algebra.

Experience

I have had my Bachelor's Degree since 1987 and have been a teacher since 1988. I earned my Masters Degree in Mathematics May 2010. I have been teaching at the same community college since 2002.

Education/Credentials
I have taught 12 years at the community college level, medical college, and technical college as well as a high school instructor and alternative education instructor and charter school instructor.

Awards and Honors
Master's GPA 3.56 Bachelor's GPA 3.34 Post grad work not degree related GPA 4.0

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