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Assuming the base as 10,prove that log...

Assuming the base as 10,prove that
`log 768+log frac(81)(32)+3log frac(5)(3)+log frac(1)(9)=3`

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KALYANI PUBLICATION-LOGARITHMS-EXERCISE
  1. Assuming the base as 10,prove that log20+7log frac(15)(16)+5log frac...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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