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If a^(2) + b^(2) = 23ab, show that : "...

If `a^(2) + b^(2) = 23ab`, show that :
`"log" (a+b)/(5) = (1)/(2) (log a + log b)`.

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ICSE-LOGARITHMS -EXERCISE 8(D)
  1. If x = log 0.6, y = log 1.25 and z = log 3 - 2 log 2, find the values ...

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  2. If a^(2) = log x, b^(3) = log y and 3a^(2) - 2b^(3) = 6 log z, express...

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  3. If "log" (a-b)/(2) = (1)/(2) (log a + log b), show that : a^(2) + b^(2...

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  4. If a^(2) + b^(2) = 23ab, show that : "log" (a+b)/(5) = (1)/(2) (log ...

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  5. If m = log 20 and n = log 25, find the value of x, so that : 2 log(x -...

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  6. Solve for x and y, if x gt 0 and y gt 0 : log xy = "log" (x)/(y) + 2...

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  7. Find x, if : (i) log(x) 625 = -4 (ii) log(x) (5x - 6) = 2.

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  8. If p = log 20 and q = log 25, find the value of x, if 2 log(x + 1) = 2...

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  9. If log(2)(x + y) = log(3)(x - y) = (log 25)/(log 0.2), find the values...

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  10. Given : (log x)/(log y) = (3)/(2) and log(xy) = 5, find the values of ...

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  11. Given log(10)x = a and log(10) y = b. (i) Write down 10^(a - 1) in t...

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  12. Solve : log(5)(x + 1) - 1 = 1 + log(5)(x - 1).

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  13. Solve for x, if : log(x)49 - log(x)7 + "log"(x)(1)/(343) + 2 = 0.

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  14. If a^(2) = log x, b^(3) = log y and (a^(2))/(2) - (b^(3))/(3) = log c,...

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  15. Given x = log(10)12, y = log(4)2 xx log(10)9 and z = log(10) 0.4, find...

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  16. Solve for x, log(x) 15 sqrt(5) = 2 - log(x) 3 sqrt(5).

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  17. Evaluate : (i) log(b)a xx log(c)b xx log(a)c (ii) log(3) 8 div log...

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  18. Show that : log(a)m div log(ab)m = 1 + log(a)b

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  19. If log(sqrt(27))x = 2 (2)/(3), find x.

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  20. Evaluate : (1)/(log(a)bc + 1) + (1)/(log(b)ca + 1) + (1)/(log(c) ab ...

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