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

Answer 1

Liam Brennan

First, you must simplify as much as possible.

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.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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