Suppose that log4 x = y where x is a positive real number.

Chapter 8, Problem 3E

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QUESTION:

Problem 3E

Suppose that log4 x = y where x is a positive real number. Find each of the following quantities.

a) log2x

b) log8x

c) log16 x

Questions & Answers

QUESTION:

Problem 3E

Suppose that log4 x = y where x is a positive real number. Find each of the following quantities.

a) log2x

b) log8x

c) log16 x

ANSWER:

Solution:

    Step 1:

            In this problem we need to  find the values of  .

           

  FORMULAS: Let a  be a real number greater than 1 . Then,

  1.  , where  x and y are positive real numbers.
  2.   , where x is a positive real number and  y is a real number.

      Let a  and b be real numbers greater than 1 , and let x be a positive real number .Then,

      3.

      4.

      5.

    Given :  where x is a positive real number.

             

             , since from formula (4).

            …………….(1)

           

  1. In this problem we need to find the value of

          From(1) , it is clear that

 

                      Therefore , .

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