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Prove that log{a+sqrt(a^2+1)}=-log{sqr...

Prove that
`log{a+sqrt(a^2+1)}=-log{sqrt(a^2+1)-a}`

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KALYANI PUBLICATION-LOGARITHMS-EXERCISE
  1. Prove that 7log frac(15)(16)+6log frac(8)(3)+5log frac(2)(5)+log fra...

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  2. Prove that log frac(384)(5)+log frac(513)(32)+log frac(5)(27)-log fr...

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  3. Prove that log{a+sqrt(a^2+1)}=-log{sqrt(a^2+1)-a}

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  4. Assuming the base as 10,prove that log frac(81)(8)-2log frac(3)(2)+3...

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  5. Assuming the base as 10,prove that log2+16log frac(16)(15)+12log fra...

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  6. Assuming the base as 10,prove that log20+7log frac(15)(16)+5log frac...

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  7. Assuming the base as 10,prove that 24 log frac(9)(10)-8log frac(24)(...

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  8. Assuming the base as 10,prove that log 768+log frac(81)(32)+3log fra...

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  9. Assuming the base as 10,prove that 23log frac(16)(15)+17log frac(25)...

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  10. Assuming the base as 10,prove that 20 log 8+45 log 16-18log 32=30(5-...

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  11. Assuming the base as 10,prove that log 12.5=2-3 log 2

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  12. Assuming the base as 10,prove that log 800=2+3 log 2

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  13. Assuming the base as 10,prove that log(1+1/2)+log(1+1/3)+log(1+1/4)+...

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  14. Assuming the base as 10,prove that (log3sqrt3+log2sqrt2-log5sqrt5)/l...

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  15. If logp/(b-c)=logq/(c-a)=logr/(a-b),then prove that p^a.q^b.r^c=1

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  16. If logx/(a+b-2c)=logy/(b+c-2a)=logz/(a+c-2b), then prove that xyz=1

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  17. If frac(xylog(xy))(x+y)=frac(yzlog(yz))(y+z)=frac(zxlog(zx))(z+x) then...

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  18. If logx/(y-z)=logy/(z-x)=logz/(x-y) prove that xyz=1

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  19. If (3.7)^x=(.37)^y=1000,then prove that 1/x-1/y=1/3

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  20. If a^2+b^2=23ab,then prove that log((a+b)/5)=1/2(log a+log b)

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