Question

Find the value of log (a^2 / bc) + log (b^2 / ac) + log (c^2 / ab) ?

Answer 1

Answer:

0

Step-by-step explanation:

log(a^2/bc)+log(b^2/ac)+log(c^2/ab)

//log(a/b)=log(a)-log(b)//

=>log(a^2)-log(bc)+log(b^2)-log(ac)+log(c^2)-log(ab)

=>log(a^2)+log(b^2)+log(c^2)-(log(bc)+log(ac)+log(ab))

=>log(a^2 b^2 c^2)-log(bc ac ab)

=>log((a^2 b^2 c^2)/(a^2 b^2 c^2))

=>log 1

=>0

Answer 2

We have to find the value of

$log\left(\frac{a^2}{bc}\right)+log\left(\frac{b^2}{ca}\right)+log\left(\frac{c^2}{ab}\right)$

some important Logarithmic identities

1. $log_a(xy)=log_ax+log_ay$
2. $log_a\left(\frac{x}{y}\right)=log_ax-log_ay$
3. $log_a(x^y)=ylog_ax$

now applying (1) to the given expression.

$log\left(\frac{a^2}{bc}\right)+log\left(\frac{b^2}{ca}\right)+log\left(\frac{c^2}{ab}\right)$

$=log\left(\frac{a^2}{bc}\times\frac{b^2}{ca}\times\frac{c^2}{ab}\right)$

$=log\left(\frac{a^2\times b^2\times c^2}{ab\times bc\times ca}\right)$

$=log\left(\frac{a^2b^2c^2}{a^2b^2c^2}\right)$

$=log1=0$

Therefore the value of

$log\left(\frac{a^2}{bc}\right)+log\left(\frac{b^2}{ca}\right)+log\left(\frac{c^2}{ab}\right)$

is 0.