SOLUTION: Find the exact value of each expression. log4(100) - log4(32) - log4(50)

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Question 209994: Find the exact value of each expression. log4(100) - log4(32) - log4(50)
Found 2 solutions by rapaljer, nerdybill:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
log4(100) - log4(32) - log4(50)

Using the Laws of Logarithms:
log%284%2C100%29+-+log%284%2C32%29+-+log%284%2C50%29
log%284%2C%28100%2F%2832%2A50%29+%29%29+
log%284%2C+%282%2F32%29%29+
log%284%2C+%281%2F16%29%29+

Now, by the basic definition of logarithms:
log+%28b%2Cx%29=y means b%5Ey=x

So, log%284%2C+%281%2F16%29%29=y+ means that 4%5Ey=1%2F16

Therefore, y = -2, since 4%5E-2=+1%2F16

I think my explanation of LOGARITHMS is easier to understand than the ones given in traditional textbooks. It's all posted free for you on my website. Just go to my website by clicking on my tutor name "Rapaljer" anywhere in algebra.com, and look for the link on my homepage that says "Basic, Intermediate, and College Algebra: One Step at a Time." Select "College Algebra" and look for "Chapter 4" which is my Logarithms chapter. You will probably need to study the Laws of Logarithms, once you understand the basic Definition of Logarithms. See also my MATH IN LIVING COLOR PAGES that correspond to this sections!

R^2

Dr. Robert J. Rapalje
Seminole Community College
Altamonte Springs Campus
Florida
R^2

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of each expression. log4(100) - log4(32) - log4(50)
.
log4(100) - log4(32) - log4(50)
log4(100/32) - log4(50)
log4(3.125) - log4(50)
log4(3.125/50)
log4(.0625)
log(.0625)/log4
-2