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If (2.3)^x=(0.23)^y=1000 then find the v...

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

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VGS PUBLICATION-BRILLIANT-REAL NUMBERS-EXERCISE 1.5
  1. Write the following expression as log N and find their values. (i) log...

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  2. Write the following expression as log N and find their values. (ii) lo...

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  3. Write the following expression as log N and find their values. (iii) 3...

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  4. Write the following expression as log N and find their values. (iv) 2l...

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  5. Write the following expression as log N and find their values. (v) log...

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

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

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

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

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  10. Expand the following. (i) log 1000

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

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

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  13. Expand the following. (iv) log""(p^2q^3)/( r )

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

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

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

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

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

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

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

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