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What is natural logarithm of this expression?

$y = 4*[x^9*x^6]$

Is it

$\ln(y) = 4 * [ 9\ln(x) + 6\ln(x)]$

or

$\ln(y) = \ln(4) + 9\ln(x) + 6\ln(x)$

Syeda
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1 Answers1

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If $y=4[x^9*x^6]$ so you have $$y=4x^{9+6}=4x^{15}$$ and so $\ln(y)=\ln(4x^{15})$ and so $$\ln(y)=\ln(4)+15\ln(x),~~x> 0$$

Mikasa
  • 67,374
  • If i have -4 instead of 4.. ln(-4) is not possible.. so it will become -ln(4)? – Syeda Dec 03 '13 at 05:47
  • @Syeda: Look at the definition of natural log. It must not be happened or be assumed unless you have other conditions for $x$. It is forbidden for ln. – Mikasa Dec 03 '13 at 05:50
  • okay, thanks!! So can I assume it -ln(4) ? Because i have negative value.. – Syeda Dec 03 '13 at 05:53
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    @Syeda: I said ln(-4x), x<0 is acceptable but if you wanna make them separate you'll walk on a ground full of mines. It 's dangerous. – Mikasa Dec 03 '13 at 05:56
  • okay!! I got it.. Thanks!! – Syeda Dec 03 '13 at 05:59