Answer :
The given logarithm, condensed into a single logarithm is log abc/4
Logarithm
From the question, we are to condense the given logarithm expression into a single logarithm
The given expression is
log c + log a/2 + log b/2
From one of the laws of logarithm, we have that
log x + log y = logxy
Thus,
log c + log a/2 + log b/2 becomes
log c × a/2 × b/2
Multiplying
Multiply the numerators first
That is,
c × a × b = cab = abc
Now,
Multiply the denominators,
2 × 2 = 4
Putting the numerator and denominators togethers, we get
abc/4
Thus,
log c × a/2 × b/2
= log abc/4
Hence, the given logarithm, condensed into a single logarithm is log abc/4
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