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According to log property $$(\log m)^n = n(\log m)$$

Which one is correct? $$(\log a)^{x+1} = (x+1)\log a$$ OR $$(\log x)^{a+1} = (a+1)\log x $$

VIVID
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Diwakar Yadav
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    Nope! The property is actually $$\log(\color{blue}{m^n}) = \color{blue} n\log(\color{blue} m)$$ – 19aksh Apr 11 '20 at 01:39
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    Neither is correct. – Andrew Chin Apr 11 '20 at 01:41
  • If you had intended on writing $\log a^x+1$, then you'd get $x\log a+1$. – Andrew Chin Apr 11 '20 at 01:41
  • Ak19 yes ...... – Diwakar Yadav Apr 11 '20 at 01:41
  • Andrew Chin According to me one of them may be right......please explain me why neither of them are correct – Diwakar Yadav Apr 11 '20 at 01:44
  • I m not satisfied with anyone of the answer.....please explain my question in details – Diwakar Yadav Apr 11 '20 at 01:55
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    Do you mean $(\log a)^{x+1}$ or $(\log a)^x+1$? And if one of your expressions is wrong, the ther one is wrong too, just swap $a$ and $x$. – Célio Augusto Apr 11 '20 at 02:02
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    According to the rest of us, neither is correct as all you have done is switch the position of the variables $a$ and $x$. To get more out of this community, please edit your question to explain your own thinking. – Andrew Chin Apr 11 '20 at 02:49
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    You should use LaTeX to prevent this kind of misunderstandings. I've tried to edit. – VIVID Apr 11 '20 at 03:05
  • Celio Augusto it is (log a)^x+1 .....and to avoid confusion the first part of ur comment...do u mean (log a)^ x+1 – Diwakar Yadav Apr 11 '20 at 04:49
  • Don’t you suppose you could try it with some chosen numbers for $a$ and $x$ ? – Lubin Apr 11 '20 at 05:04
  • Lubin is (log a)^x+1 = x+1(log a ) is correct?or (log x)^a+1 = a+1(log x) is correct ? – Diwakar Yadav Apr 11 '20 at 05:35
  • You should use LaTeX, and parentheses (where needed), and also use superscripts correctly, to prevent this kind of misunderstanding. Do you mean $((\log a)^x)+1$ or $(\log a)^{x+1}$ or $\log(a^{x+1})$? Only the last of these is equal to $(x+1)\log a$. – Rosie F Apr 11 '20 at 06:35
  • Rosie F Read my question .....it has two question ....among two of them which one is correct question no 1 is (log a) ^x+1 = x+1 (log a) Is my answer x+1 (log a) is correct ? And question no 2 is (log x)^a+1 = a+1(log x) is my answer a+1(log x) is correct ? Now tell me which one is correct from 1 and 2 and why – Diwakar Yadav Apr 11 '20 at 07:10

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