anonymous
  • anonymous
Logarithm question
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[7\ln \left| \frac{ x+\sqrt{x^{2} - 7} }{ \sqrt{7} } \right| = 7(\ln \left| x+\sqrt{x ^{2}-7} \right| -\ln \sqrt{7} \]
yamyam70
  • yamyam70
are we asked to prove?
IrishBoy123
  • IrishBoy123
you're missing a bracket and call that numerator inside the log something like "A" and re-write it again. it might look way less foreboding

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rishavraj
  • rishavraj
\[\log a^x = x \log a~~~~ and ~~~~ \log a - \log b = \log \frac{ a }{ b }\]
dinamix
  • dinamix
hey ln|x|= ln x i mean u can remove it
dinamix
  • dinamix
proof|dw:1440351441869:dw|
mathmate
  • mathmate
In any case, the following is an identity, use the standard identities given by @rishavraj to prove the followin: \(\large 7\ln \left| \frac{ x+\sqrt{x^{2} - 7} }{ \sqrt{7} } \right| = 7(\ln \left| x+\sqrt{x ^{2}-7} \right| -\ln \sqrt{7})\)
dinamix
  • dinamix
@mathmate @IrishBoy123 my prove i draw it right ;p
amistre64
  • amistre64
ln|x| and ln x do not have the same domain, therefore they are not the same
IrishBoy123
  • IrishBoy123

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