1

Logarithm


log5 base3 = x and log11 base25=y then value of log(11÷3) base3 in terms of x and y is ? 


12-May-2016 12:23 PM
~2

Answers (1)


0

Using the basic log properties like:

  1. logb(x/y) = logb(x) - logb(y)
  2. logb(xy) = y * logb(x)
  3. logb(x) = logc(x) / logc(b)
  4. logb(b) = 1
  5. logb(c) = 1 / logc(b)
  6. logbp(x) = (1/p) * logb(x)  ---> (base was in power p)

=> Given

log3(5) = x

=> log5(3) = 1/x -------(property (5)

and

log25(11) = y

= log52(11) = y

= (1/2) * log5(11) = y   -------(property (6)

= log5(11) = 2y

 

To find:

log3(11/3)

= log3(11) - log3(3)  ------(using property (1)

= log3(11) - 1 --------(property (4))

= [ log5(11) / log5(3) ] -1 ---------(property (3)

=\frac{2y}{1/x} - 1

= 2xy -1

 

 

 



13-05-2016 13:07
~4

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