If x-0- y-0- then log x y is equal toA- log -x-log -yB- -log x-log yC- log x-log yD- log x-log y

The correct option is A log( x) + log( y) log xy = log|x | + log |y | log xy = log( x) + log( y) [Because x 0, |x | = x, y 0, |y | = y ] ...

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Logarithmic Inequalities

If x<0, y<0, ...

Question

If $x < 0$ , $y < 0$ , then $l o g (x y)$ is equal to _______________ .

log x + log y

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log(-x) + log(-y)

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- log x - log y

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log x - log y

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Solution

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∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & l o g_{x} y & l o g_{x} z l o g_{y} x & 1 & l o g_{y} z l o g_{z} x & l o g_{z} y & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

log(x-y)=logx-logy

x

y

z

> 0

1

log x + log y + log z = 0

x^{\frac{1}{log y} + \frac{1}{log z}} \times y^{\frac{1}{log z} + \frac{1}{log x}} \times z^{\frac{1}{log x} + \frac{1}{log y}}

10

logx+ log( xy⁸)/(log x)²+(log y)²=2 & logy+log(x⁸/y)/(log x)²+(log y)²=0( where base of log is 10 ) compute the product of(xy).

l o g (\frac{x + y}{6}) = \frac{1}{2} (l o g x + l o g y)

\frac{x}{y} + \frac{y}{x} = 34

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