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If a^(4) + b^(4) = 14 a^(2)b^(2), then s...

If `a^(4) + b^(4) = 14 a^(2)b^(2)`, then show that `log(a^(2) + b^(2)) = log a + log b + 2 log 2`.

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CALCUTTA BOOK HOUSE-LOGARITHM-Examples (Long-answer type question)
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  10. If log((x+y)/5) = 1/2 (log x + log y), then show that x/y + y/x = 23.

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  11. If a^(4) + b^(4) = 14 a^(2)b^(2), then show that log(a^(2) + b^(2)) = ...

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  12. If (log x)/(y-z) = (log y)/(z-x) = (log z)/(x-y), then prove that xyz ...

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  13. If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b), then prove that x...

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  14. If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b), then prove that x^...

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  15. If a^(3-x).b^(5x) = a^(5+x).b^(3x), then show that x log (b/a) = log a...

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  16. Show that the value of log(10)2 lies in between 1/4 and 1/3.

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  17. Solve : (i) log(8)[log(2){log(3)(4^(x)+17)}] = 1/3

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  18. Solve : log(8)x+log(4)x+log(2)x=11

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  19. Solve : (iii) 4^(log(9^3))+9^(log(2^4))=10^(log(x^83))

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  20. Solve : (iv) log(10)x - log(10)sqrt(x) = 2/(log(10)x)

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