Alex C.

asked • 07/14/16

Using logarithmic identities to evaluate

Hi, I am very confused on solving the following. I really have no idea how to solve it and Im freaking out. 
 
a) 8 raised to -log822
b) (log10)3
c) √ln1
d) log(2/3)(27/8)
e) 7 raised to 2log77 + 3log72
 
I know Im asking for alot but this is really making me nervous. I really want to know how to do it.

James B.

You will get better and quicker responses if you submit these as individual questions.
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07/14/16

Alex C.

Thank you!
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07/14/16

Kenneth S.

e) 7 raised to 2log77 + 3log72
First, combine: the exponent (logarithm!) can be written as log7[73•23];
now when 7 is raised to this exponent, the result is just the number in square brackets, namely 8•49 = 392
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07/14/16

Kenneth S.

c) √ln1 means take the square root of  ( ln 1).
Ask yourself what is the natural log of 1. Hint: eo = 1.
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07/14/16

1 Expert Answer

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Kenneth S. answered • 07/14/16

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a) 8 raised to -log822  is just 22-1 or 1/22 because exponentiating, base 8, using logarithm, base 8, are inverse operations

b) (log10)3 = 13 = 1
 
The key to all of these is understanding the 3 basic laws of logarithms (a.k.a. properties)
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