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Evaluate each of the following in terms of x and y, if it is given `x=log_(2)3 and y=log_(2) 5.` (iv) `log_(2)6750`

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VGS PUBLICATION-BRILLIANT-REAL NUMBERS-EXERCISE
  1. Evaluate each of the following in terms of x and y, if it is given x=...

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  2. Evaluate each of the following in terms of x and y, if it is given x=...

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  3. Evaluate each of the following in terms of x and y, if it is given x=...

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  4. Evaluate each of the following in terms of x and y, if it is given x=...

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  5. Expand the following. (i) log 1000

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  6. Expand the following. (ii) log[128/625]

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  7. Expand the following. (iii) log x^2y^3z^4

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  8. Expand the following. log((p^2q^3)/r^4)

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  9. Expand the following. (v) log sqrt((x^3)/(y^2))

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  10. If x^2+y^2=25xy. then prove that 2log(x+y)=3log3+logx+logy.

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  11. If log((x+y)/(3))=1/2(logx+logy), then find the values of (x)/(y)+(y)/...

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  12. If (2.3)^x=(0.23)^y=1000 then find the value of (1)/(x)-(1)/(y).

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  13. If 2^(x+1)=3^(1-x) then find the value of x.

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  14. Is (i) log 2 is rational or irrational ? Justify your answer.

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  15. Is (ii) log 100 is rational or irrational ? Justify your answer.

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  16. Can the number 6^n, n being a natural number, end with the digit 5 ? G...

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  17. Is 7xx5xx3xx2+3 a composite number ? Justify your answer.

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  18. Prove that (2sqrt3+sqrt5) is an irrational number. Also check whether ...

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  19. If x^2 + y^2 = 6xy , prove that 2 log (x + y) = logx + logy + 3 log 2

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  20. Find the number of digit in 4^(2013), if log(10)2=0.3010.

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