Some simple logarithms ?

Question

Hello,

Could someone kindly outline the procedure needed to evaluate the following:

a) 4 log₉ 3

b) 4 log₃ 1/27

Kind regards!!

Answer 1

a.) This expression does not have an even answer. When you plug it into a calculator you get 6.34

b.)  This one is doable.  First remember that 1/27 is the same as 27^-1.

Which means you can pull the negative one out of the log leaving you you with   -4*log₃27.

Now it is only a matter of realizing that 3 cubed is 27  so the final answer is -12

Answer 2

a) 4 log₉ 3 = 4  log₉ 9^(1/2)

=4 (1/2)  log₉ 9 = 2

b)4 log₃ (1/3)^3

= 4  3 log₃ (1/3)

=12 [ - log₃ 3]

=-12