Maths-
General
Easy

Question

Given that log subscript p space x equals alpha and log subscript g space x equals beta then value of log subscript p divided by q end subscript space x equals –

  1. fraction numerator alpha beta over denominator beta minus alpha end fraction
  2. fraction numerator beta minus alpha over denominator alpha beta end fraction
  3. fraction numerator alpha minus beta over denominator alpha beta end fraction
  4. fraction numerator straight a beta over denominator alpha minus beta end fraction

The correct answer is: fraction numerator alpha beta over denominator beta minus alpha end fraction


    Here we have to find the value of  log subscript p divided by q end subscript space x if log subscript q space x equals beta and log subscript p space x equals alpha.
    { We know that bold italic l bold italic o bold italic g subscript bold a bold italic b bold space bold equals fraction numerator bold space bold 1 over denominator bold space bold l bold o bold g subscript bold b bold a end fraction bold. }
    log subscript p space x equals alpha Also we can write as 1 over alpha space equals space log subscript x p And ,
    log subscript q space x equals beta Also we can write as 1 over beta space equals space log subscript x q.
    log subscript x p space minus space log subscript x q space equals fraction numerator beta space minus space alpha over denominator alpha beta end fraction
log subscript x bevelled p over q space equals fraction numerator beta space minus space alpha over denominator alpha beta end fraction space space space space space space space space space space space left curly bracket space bold italic l bold italic o bold italic g subscript bold a bold italic b bold space bold equals fraction numerator bold space bold 1 over denominator bold space bold log subscript bold b bold a end fraction space right curly bracket
log subscript bevelled p over q end subscript x space equals fraction numerator alpha beta over denominator beta space minus space alpha end fraction space space
    If a, m and n are positive integers and a ≠ 1, then;
    log subscript a m over n space equals log subscript a m space minus space log subscript a n
    Thus, the log of two numbers m and n, with base ‘a’  is equal to the sum of log m and log n with the same base ‘a’.

    These four basic properties all follow directly from the fact that logs are exponents. 
    logb(xy) = logbx + logby.
    logb(x/y) = logbx - logby.
    logb(xn) = n logbx.
    logbx = logax / logab.

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