Sure, here are the simplified expressions using the properties of logarithms:

a) log39 + log327
Using the property loga + logb = log(ab), we get:
log(39*327) = log12753

b) log28 - log22
Using the property loga - logb = log(a/b), we get:
log(28/22) = log1.2727

c) 3log105 - log1025
First, use the property n*loga = log(a^n) on 3log105 to get log(105^3). Then, use the subtraction property:
log(105^3/1025) = log(1157625/1025) = log1129.878

d) lnx + lny
Using the property ln(a) + ln(b) = ln(ab), we get:
ln(xy)

e) loga^an
Using the property n*loga = log(a^n), we get:
log(a^an) = log(a^(a^n))

Question

Sure, here are the simplified expressions using the properties of logarithms:

a) log39 + log327
Using the property loga + logb = log(ab), we get:
log(39*327) = log12753

b) log28 - log22
Using the property loga - logb = log(a/b), we get:
log(28/22) = log1.2727

c) 3log105 - log1025
First, use the property n*loga = log(a^n) on 3log105 to get log(105^3). Then, use the subtraction property:
log(105^3/1025) = log(1157625/1025) = log1129.878

d) lnx + lny
Using the property ln(a) + ln(b) = ln(ab), we get:
ln(xy)

e) loga^an
Using the property n*loga = log(a^n), we get:
log(a^an) = log(a^(a^n))

Knowee AI · Accepted Answer

Sure, here are the simplified expressions using the properties of logarithms:

a) log39 + log327
Using the property loga + logb = log(ab), we get:
log(39*327) = log12753

b) log28 - log22
Using the property loga - logb = log(a/b), we get:
log(28/22) = log1.2727

c) 3log105 - log1025
First, use the property n*loga = log(a^n) on 3log105 to get log(105^3). Then, use the subtraction property:
log(105^3/1025) = log(1157625/1025) = log1129.878

d) lnx + lny
Using the property ln(a) + ln(b) = ln(ab), we get:
ln(xy)

e) loga^an
Using the property n*loga = log(a^n), we get:
log(a^an) = log(a^(a^n))

Apply the properties of logarithms to simplify the expressions: (Criteria A)a) log39+log327b) log28−log22c) 3log105−log1025d) lnx+lnye) logaan

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