Question

What is the condensed form of `log_w 5 - 2log_w a + 3log_2b - 4log_wc`?

Answer 1

First, you must simplify as much as possible.

Explanation:

Use the property `alog_nx = log_nx^a`:

`log_w5 - log_wa^2 + log_2b^3 - log_wc^4`

You can use the property `log_an - log_am = log_a(n/m)` to simplify the logs that are in base `w`.

`log_w((5/a^2)/c^4) + log_2b^3`

= `log_w(5/(a^2c^4)) + log_2b^3`

This is the simplest form, since we can't combine logs of unequal bases.