## anonymous one year ago Logarithm question

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1. anonymous

$7\ln \left| \frac{ x+\sqrt{x^{2} - 7} }{ \sqrt{7} } \right| = 7(\ln \left| x+\sqrt{x ^{2}-7} \right| -\ln \sqrt{7}$

2. yamyam70

3. 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

4. rishavraj

$\log a^x = x \log a~~~~ and ~~~~ \log a - \log b = \log \frac{ a }{ b }$

5. dinamix

hey ln|x|= ln x i mean u can remove it

6. dinamix

proof|dw:1440351441869:dw|

7. mathmate

In any case, the following is an identity, use the standard identities given by @rishavraj to prove the followin: $$\large 7\ln \left| \frac{ x+\sqrt{x^{2} - 7} }{ \sqrt{7} } \right| = 7(\ln \left| x+\sqrt{x ^{2}-7} \right| -\ln \sqrt{7})$$

8. dinamix

@mathmate @IrishBoy123 my prove i draw it right ;p

9. amistre64

ln|x| and ln x do not have the same domain, therefore they are not the same

10. IrishBoy123

+1 @amistre64