Question

Use the multiplication law for logarithm to expand the following expression:
`log_(8) (21)`

- worth 20pt

Answer 1

`\log_8{(3)} + \log_8{(7)}`

Explanation:

Product Rule for Logarithms

`\log_b{(mn)} = \log_b{(m)} + \log_b{(n)}`

Instead of 21 you can write 3 · 7, because 21 = 3 · 7.

`\log_8{(21)} = \\= \log_8{(3 \cdot 7)} =\\= \log_8{(3)} + \log_8{(7)}`