SOLUTION: write the expression as the logarithm of a single quantity: 2ln8 + 5lnz

Question 224326: write the expression as the logarithm of a single quantity:
2ln8 + 5lnz
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
You need to move the coefficients of each term to the exponent:

Now, the sum of two logarithms becomes the log of a product:

I have a complete explanation of LOGARITHMS on my website that you may find helpful!! To find my website, do a "Bing" Search for my last name "Rapalje". Look for "Rapalje Homepage" near the top of the search list. Then, near the top of my Homepage, look for "Basic, Intermediate and College Algebra: One Step at a Time," select "College Algebra" and then "Chapter 4". "Section 4.03 Laws of Logarithms" is the section that directly relates to this problem! You REALLY need to GET this section. If you don't understand the Laws of Logarithms, then you will NEVER understand logarithm problems. I think I have an explanation here that is absolutely unlike the ones in traditional College Algebra books. This is my own non-traditional explanation, and I believe if you STUDY this chapter, and watch my FREE videos that you can get from my website, you too will understand this intimidating chapter. In addition to my explanations, examples and exercises, I have my "MATH IN LIVING COLOR" pages where I solved many of these exercises IN COLOR!!

To see the TWO 2-hour videos filmed in my own classes a few years ago FREE, look on my Homepage for "Rapalje Videos in Living Color". Select College Algebra, and look for Logarithms Part I and Logarithms Part II. I must apologize that the videos are a few years old, and my calculator explanation is VERY out of date!!

R^2

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamone Springs Campus

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