Question

Expand the logarithmic expression.

Answer 1

Hello from MrBillDoesMath!

Answer: The third choice

Discussion:

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

for positive number a and b.

In our case this translates to:

log {8} ( a/2) = log {8} (a) - log{8} (2)

where log {8}, note curly braces not parentheses, mean "base 8

This is the third choice.

Thank you,

MrB

Answer 2

If two values are divided by each other inside a logarithm, then we can expand the logarithm into the difference of two separate logarithms.

This is the second law of logarithms.

So we can rewrite this as log₈ a - log₈ 2.