Question

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Answer 1

Answer:

This is the answer of your question

Answer 2

Topic :-

Logarithms

Given to prove that :-

$\dfrac{1}{log_xxyz} +\dfrac{1}{log_yxyz} +\dfrac{1}{log_zxyz} =1$

Solution :-

As we know the properties of logarithms ,

Interchange formula :- $log_ab= \dfrac{1}{loga_b}$

So, by using this property we get ,

$\dfrac{1}{log_xxyx} = log_{xyz} x$

$\dfrac{1}{log_yxyz} = log_{xyz}y$

$\dfrac{1}{log_zxyz} = log_{xyz}z$

$= logx_{xyz} + logy_{xyz}+logz_{xyz}$

As also we know that , product formula :-

$log_amnp= logm_a +logn_a +logp_a$

$= logxyz_{xyz}$As also we know that $loga_a = 1$

So, $= logxyz_{xyz} =1$

So,

${\boxed{\dfrac{1}{log_xxyz} +\dfrac{1}{log_yxyz} +\dfrac{1}{log_zxyz} =1}}$

Hence proved !

Used properties:-

$loga_a = 1$

$log_ab= \dfrac{1}{loga_b}$

$log_amnp= logm_a +logn_a +logp_a$

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