Question

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$\frac{ log \: 2}{p} + \frac{ log \: 3}{p} + \frac{ log \: 6 }{p}$
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Answer 1

Answer:

Using some logarithmic identities given logarithmic expression can be expressed in its simplest form as shown in the solution,

General identities:-)

$log(m) + log(n) = log(m.n) \\ \\ log(m) {}^{n} = n \times log(m)$

Using above identities given expression

$\frac{ log \: 2 }{p} + \frac{log \: 3}{p} + \frac{log \: 6}{p}$

can be expressed as,

$\: \: \: \: \frac{ log \: 2 }{p} + \frac{log \: 3}{p} + \frac{log \: 6}{p} \\ \\ = \frac{log \:2 + log \: 3 + log \: 6}{p} \\ \\ = \frac{log(2.3.6)}{p} \\ \\ = \frac{log \: 36}{p} \\ \\ = \frac{ log(6) {}^{2} }{p} \\ \\ = \frac{2log \: 6}{p}$

Here the given logarithmic expression is in its simplest form .

Answer 2

${\huge{\tt QuestioN}}$

$\frac{ log \: 2}{p} + \frac{ log \: 3}{p} + \frac{ log \: 6 }{p}$

${\huge{\tt AnsweR}}$

Using the identities we get the answer:

= log( m ) + log( n ) = log( m.n )

= log( m )^n = n × log( m )

= log2 / p + log3 / p + log6 / p

= log2 + log3 + log6 / p

= log ( 2.3.6 ) / p

= log36 / p

= log ( 6 )² / p

= 2log 6 / p