<PRE><B>Question 20546</B>
log&lt;sub&gt;7&lt;/sub&gt;X + log&lt;sub&gt;7&lt;/sub&gt;X = log&lt;sub&gt;7&lt;/sub&gt;12 + log&lt;sub&gt;7&lt;/sub&gt;3
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The two terms on the left are just alike so when you add them you just get 2 of
them!  That is, log&lt;sub&gt;7&lt;/sub&gt;x + log&lt;sub&gt;7&lt;/sub&gt;x = 2·log&lt;sub&gt;7&lt;/sub&gt;x. So now you have
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2·log&lt;sub&gt;7&lt;/sub&gt;X = log&lt;sub&gt;7&lt;/sub&gt;12 + log&lt;sub&gt;7&lt;/sub&gt;3
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Use the rule N·log&lt;sub&gt;B&lt;/sub&gt;U = log&lt;sub&gt;B&lt;/sub&gt;U&lt;sup&gt;N&lt;/sup&gt; on the left
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log&lt;sub&gt;7&lt;/sub&gt;X&lt;sup&gt;2&lt;/sup&gt; = log&lt;sub&gt;7&lt;/sub&gt;12 + log&lt;sub&gt;7&lt;/sub&gt;3
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Now use the rule log&lt;sub&gt;B&lt;/sub&gt;U + log&lt;sub&gt;B&lt;/sub&gt;V = log&lt;sub&gt;B&lt;/sub&gt;UV
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log&lt;sub&gt;7&lt;/sub&gt;X&lt;sup&gt;2&lt;/sup&gt; = log&lt;sub&gt;7&lt;/sub&gt;(12·3)
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Now raise both sides to the 7 power, which is the same as dropping the logs.
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X&lt;sup&gt;2&lt;/sup&gt; = 36
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X = ±6, but we cannot take logs of negative numbers, so the answer is X = 6
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Edwin
AnlytcPhil@aol.com</PRE>