Use the properties of logarithms to simplify the expression.

Question

Use the properties of logarithms to simplify the expression. ​  ​

Quizplus · Accepted Answer

Using the property that log_m(n) - log_m(r) = log_m(n/r) and log_m(n^p) = plog_m(n), we can simplify the expression as follows:

log_6(19) - log_6(11) - log_6(7) + log_6(2) 
= log_6(19/11) - log_6(7) + log_6(2) 
= log_6(1.727) - log_6(7) + log_6(2) 
= log_6(1.727/7) + log_6(2) 
= log_6(0.247) + log_6(2) 
= log_6(0.247*2) 
= log_6(0.494)

Now, we can use the fact that log_m(1) = 0 for any base m, so log_6(0.494/0.494) = log_6(1) = 0. Therefore, the answer is 5, which corresponds to choice E.

Use the Properties of Logarithms to Simplify the Expression