Question

solve for log
if you know only then​

Answer 1

Topic:-

Logarithms

Given to find the value of :-

$log_{10}\dfrac{bc}{a^2} +log_{10}\dfrac{ac}{b^2} +log_{10}\dfrac{ab}{c^2}$

Solution :-

As we know that ,

$logmnp_{10}= logm_{10} +logn_{10}+logp_{10}$

So,

$log_{10}\dfrac{bc}{a^2} +log_{10}\dfrac{ac}{b^2} +log_{10}\dfrac{ab}{c^2}$

$= log_{10}\dfrac{bc}{a^2} \times \dfrac{ac}{b^2} \times\dfrac{ab}{c^2}$

$= log_{10}\dfrac{\not{b}\not{c}}{\not{a^2}} \times\dfrac{\not{a}\not{b}}{\not{b^2}} \times\dfrac{\not{a}\not{b}}{\not{c^2}}$

$= log1_{10}$

As we know that = $log1_{10}$ is 0

$=0$

So, the value of $log_{10}\dfrac{bc}{a^2} +log_{10}\dfrac{ac}{b^2} +log_{10}\dfrac{ab}{c^2}$ = 0

So, option b is the correct

Used properties:-

$logmnp_{10}= logm_{10} +logn_{10}+logp_{10}$

$log1_{10} = 0$

Know more properties :-

$log_{a}\bigg(\dfrac{m}{n} \bigg)= log m_a- logn_{a}$

$log_aa= 1$

$log_{a}m^{n} = nlog_am$

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