Please help me with this question Use properties of logarith

Please help me with this question:

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. (please show work)

Solution

Log Properties: logA +logB = log(A*B)

logA - logB = logA/B

Part-I

a) log6(7) + log6(7*11) = log6(7*7*11) = log6(539)

b) log6(7) -log6(11) = log611/7)

c) log6(7)*log6(11) = log6(7)*log6(11) no change

d) log6(77) = log6(7*11) = log6(7) +log6(11)

Part-II

a) -d*log9(x) = log9(x^-d)

b) -9*logd(x) = logd(x^-9)