Question

show that log (x^2/yz) + log(y^2/zx) + log (z^2/xy) = 0​

Answer 1

$\;\;\underline{\textbf{\textsf{ To Prove :-}}}$

• $\sf \log( \frac{x {}^{2} }{yz} ) + \log( \frac{y {}^{2} }{zx} ) + \log( \frac{z {}^{2} }{xy}) = 0$

$\;\;\underline{\textbf{\textsf{ Proof :-}}}$

LHS

$\sf log( \frac{x {}^{2} }{yz} ) + log( \frac{y {}^{2} }{zx} ) + log( \frac{z {}^{2} }{xy} )$

$\sf \dashrightarrow log(x {}^{2} ) - log(yz) + log(y {}^{2} ) - log(zx) + log(z {}^{2} ) - log(xy)$

$\sf \dashrightarrow logx {}^{2} + logy {}^{2} + logz{}^{2} - ( \log \: xy + \log \: yz + \log \: zx)$

$\sf \dashrightarrow \log(x {}^{2} y {}^{2} z {}^{2} ) - \log(xy \times yz \times zx)$

$\sf \dashrightarrow \log(x {}^{2}y {}^{2} z {}^{2}) - \log(x {}^{2} y {}^{2} z {}^{2} )$

$\sf \dashrightarrow 0$

$\sf \dashrightarrow RHS$

ㅤ

ㅤ$\;\;\underline{\textbf{\textsf{ Hence-}}}$

(Proved)

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

ㅤ$\;\;\underline{\textbf{\textsf{ Need to Know -}}}$

$\sf1) \log x + \log \: y = \log \:xy$

$\sf2) \log( \frac{x}{y}) = \log \: x - \log \: y$

$\sf3) \log \: x {}^{n} = n \log \:x$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

Yeahhhhhhhhhhh

Mark me as brainliest