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Prove: logb b^x=x...

Prove: `log_b b^x=x`

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log_x (a/b) =….

A : (a-b)/(a)+(1)/(2)((a-b)/(a))^(2)+(1)/(3)((a-b)/(a))^(3)+....=log_(e)((a)/(b)) R : log_(e)(1-x)=-x-(x^(2))/(2)-(x^(3))/(3)-(x^(4))/(4)-....

VGS PUBLICATION-BRILLIANT-REAL NUMBERS-EXERCISE
  1. Prove: logb b = 1

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  2. Prove: logb1 = 0

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  3. Prove: logb b^x=x

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  4. Prove: If logx16 = 2, then x^2 = 16 implies x = +- 4, Is it correct or...

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  5. We know that log10 100000 = 5 Show that you get the same answer by wri...

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  6. Express the logarithms of the following into sum of the logarithms. (i...

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  7. Express the logarithms of the following into sum of the logarithms. (i...

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  8. Express the logarithms of the following into sum of the logarithms. (i...

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  9. Theorem : (Quotient Rule) Let a, x and y be positive real numbers wher...

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  10. Express the logarithms of the following into difference of the logarit...

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  11. Express the logarithms of the following into difference of the logarit...

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  12. Express the logarithems of the following into difference of the logari...

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  13. Express the logarithms of the following into difference of the logarit...

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  14. We know that (a^m)^n = a^(mn) Let a^m = x, then m = logax x^n = a^(mn)...

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  15. We have log(2)32 = 5 . Show that we get the same result by writing 32 ...

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  16. Using logax^n = n loga x, expand the following :log2^7^25.

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  17. Note : log x = log10 x: log27^25

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  18. Note : log x = log10 x: log58^50

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  19. Note : log x = log10 x: log 5^23

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  20. Note : log x = log10 x: log 1024

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