Condense each expression to a single logarithm: log6 12+ log6 5 + 3log6 7 The 6, 6 and the 7 are at the bottom of the log.

Expert Answers
mariloucortez eNotes educator| Certified Educator

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)`

                                                      `=log_6 20580`   

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.

oldnick | Student

`log_6(12) +log_6(5)+3log_6(7)=`

`=log_6(12)+log_6(5)+ log_6(7^3)=`


`=log_6[(12)(5)(343)]=log_6(20580) `