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

First some background log info:

log (base a) b = x, is the same thing as a^x = b

Also, if you can somehow manage to get the base (the "a") to be the same value as the "b", then the result is 1.  In other words:

log (base a) a = 1

a)  4 log (base 9) 3

= 2 log (base 9) (3^2)

= 2 log (base 9) 9

= 2 * 1

= 2

b)  4 log (base 3) (1/27)

= - 4 log (base 3) 27  (if you reciprocate the inside, it just changes the sign of the whole log function)

= - 4 log (base 3) (3^3)

= - 12 log (base 3) 3

= -12 * 1

= -12

Answer 2

Tip

Ensure that questions make sense.

In this case the log bases are missing.

It may not be your fault but it is up to you to check.

Answer 3

a)log base 9 to the 3^4

thats a log property

3^4=81

log base 9 to the 81=2

b)4 log base 3 to the 1/27

log base 3 to the 1/27=3

4*3=12