Advanced Math/Logarithm

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Expert: Sherry Wallin - 12/7/2008


Question
I am just a bit confuse about this problem, could you please assist..
Here is the problem: Write the expression as a single logarithm.

2ln(x^2+1)-ln(2x^3-1).

Answer
Hi Annie~
First off this is a difference of two logs of the same base so you can write it as a quotient of the logs but you have 2 of the first [2*ln(x^2 1)] which can be brought to be the power of the argument so let's do that first.
2ln(x^2 1)-ln(2x^3-1) = ln(x^2 1)^2-ln(2x^3-1)= ln[((x^2 1)^2)/(2(x^3)-1)]
= ln{x^4 2x^2 1)/[2(x^3)-1]
Either one of these last two expressions are equivalent. They didn't ask you to simplify just to write as a single logarithm which they both are. The first one should be sufficient.

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Sherry Wallin

Expertise

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

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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.

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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.

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

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