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If frac(xylog(xy))(x+y)=frac(yzlog(yz))(...

If `frac(xylog(xy))(x+y)=frac(yzlog(yz))(y+z)=frac(zxlog(zx))(z+x)` then show that `x^x=y^y=z^z`

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

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

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

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

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

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

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  7. If x^2+y^2=7xy,then prove that log(x+y)=log3+1/2(logx+logy)

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  8. If x^2+y^2=11xy,then prove that log((x+y)/13)=1/2(logx+logy)

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  9. If a^2+b^2=18ab,then prove that log((a-b)/4)=1/2(loga+logb)

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  10. If 4a^4+9b^4=37a^2b^2,then prove that log(2a^2+3b^2)=loga+logb+log7

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  11. If 2log(a+b)=loga+logb+log8,then prove that (a+b)^2=8ab

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  12. If log((x+y)/3)=1/2(logx+logy),then prove that x/y+y/x=7

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  13. If log((a+2b)/4)=1/2(loga+logb),then prove that a^2+4b^2=12ab

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  14. If log((x+y)/2)=1/2(logx+logy),then prove that x=y

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  15. Given that log10 2=.3010,log10 3=.4771,log10 4=.6021,log10 5-.6990,log...

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  16. Given that log10 2=.3010,log10 3=.4771,find the value of log10 12

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  17. Given that log10 2=.3010,log10 3=.4771,log10 4=.6021,log10 5-.6990,log...

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  18. Given that log10 2=.3010,log10 3=.4771,log10 4=.6021,log10 5-.6990,log...

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  19. Given that log10 2=.3010,log10 3=.4771,then find the value of log10 (...

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  20. Given that log10 2=.3010,log10 3=.4771,log10 4=.6021,log10 5-.6990,log...

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