SOLUTION: Which one of the following is true? (1) log(7+3)=log7+log3 (2) (log10)^3=3log10 (3) ln(7e^10)=10+ln7 ? HELP.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Which one of the following is true? (1) log(7+3)=log7+log3 (2) (log10)^3=3log10 (3) ln(7e^10)=10+ln7 ? HELP.      Log On


   

Question 202241: Which one of the following is true? (1) log(7+3)=log7+log3 (2) (log10)^3=3log10 (3) ln(7e^10)=10+ln7 ? HELP.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
laws of logarithms:
1. log+%28x%2Ay%29+=+log%28x%29+%2A+log%28y%29
2. log%28x%2Fy%29+=+log%28x%29+-+log%28y%29
3. log%28x%5Ey%29+=+y%2Alog%28x%29
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looking at your number 1:
log%287%2B3%29+=+log%287%29+%2B+log%283%29
this doesn't follow any rule above.
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looking at your number 2:
log%2810%5E3%29++=+3%2Alog%2810%29
this looks like it follows rule # 3 above.
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looking at your number 3:
ln%287e%5E10%29+=+10+%2B+ln%287%29
can't say this looks like any of the basic rules of logarithms.
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even though I'm not sure you wrote it correctly, number 2 is the only one that looks like it might be true.
The others don't look right.
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Answer by ikleyn(52925) About Me  (Show Source):
You can put this solution on YOUR website!
.
Which one of the following is true?
(1) log(7+3)=log7+log3
(2) (log10)^3=3log10
(3) ln(7e^10)=10+ln7 ? HELP.
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        The answers in the post by @Theo are incorrect.

        His writing is so confusing that it is difficult to comment on.

        I came to bring correct answers. 


Question (1).  Left side is  log(10) = 1.

               Right side, due to the logarithm rules,  is log(7*3) = log(21).

               log(10) and log(21) are different expressions, not identical and not equal.

               Hence, formula (1) is wrong.



Question (2).  Left side is  (log(10))^3 = 1^3 = 1.

               Right side is  3log(10) = 3*1 = 3.
  
               Thus, left side and right side represent different numbers,

               so, formula (2) is wrong.



Question (3).  Left side is  ln(7) + ln(e^10) = ln(7) + 10.

               Right side is 10 + ln(7), which is the same as  ln(7) + 10.

               So, we conclude that formula (3) is correct.


ANSWER.  Of the three formulas, only (3) is true.  Others are wrong.

Solved.

Ignore the post by @Theo for the peace in your mind.