Question

5. Use the properties of logarithms to expand log₂

constant multiple of variables. (Assume all variables are positive.)
as a sum, difference, and/or

Answer 1

1/2log₂(a-1) -log₂(9)

Explanation:

You want the expanded form of log₂(√(a-1)/9).

Rules of logarithms

The relevant rules of logarithms are ...

log(a^b) = b·log(a)

log(a/b) = log(a) -log(b)

The rules are applicable for any base.

Application

`\log_2{(√(a-1))/(9)}=\log_2{(√(a-1))}-\log_2{(9)}=\boxed{(1)/(2)\log_2{(a-1)}-\log_2{(9)}}`