Question 202241
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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.



<pre>
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.


<U>ANSWER</U>.  Of the three formulas, only (3) is true.  Others are wrong.
</pre>

Solved.


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