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Condense each expression to a single logarithm: log6 12+ log6 5 + 3log6 7 The 6, 6 and...
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High School Teacher
The properties logarithm that can be applied here are:
`nlog_b a =log_b a^n`
`log_b a + log_b c = log_b (ac)`
Notice that the properties will only apply if the terms have the same bases (the small number beside the log). Are you sure that the 7 is at the bottom of the log? I assume that you just mistyped it and it should be 6 at the bottom of the log on the third term.
First, apply the first property on the third term:
`3log_6 7 = log_6 7^3`
*`7^3 = 343`
`3log_6 7 = log_6 343`
So, you have:
`log_6 12 + log_6 5 + log_6 343`
Then apply the second property:
`log_6 12 + log_6 5 + log_6 343 = log_6 (12*5*345)`
So the answer is `log_6 20580` .
If your problem is just you said that 7 on the tird term is at the bottom of log, you can apply the same properties but it will not be a single logarithmic expression.
Posted by mariloucortez on April 15, 2013 at 11:57 PM (Answer #2)
Posted by oldnick on April 15, 2013 at 11:50 PM (Answer #1)
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