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

Question

Apply the properties of logarithms to simplify the expressions:

(Criteria A)

a) log_3 9 + log_3 27
b) log_2 8 - log_2 2
c) 3 log_{10} 5 - log_{10} 25
d) ln x + ln y
e) log_a a^n

🧐 Not the exact question you are looking for?Go ask a question

Solution

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))

This problem has been solved

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.

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

Question