What is expand log_{11}((sqrt(x+y))/(x^2y)) ?

The solution to expand log_{11}((sqrt(x+y))/(x^2y)) is log_{11}(sqrt(x+y))-2log_{11}(x)-log_{11}(y)

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expand log_{11}((sqrt(x+y))/(x^2y))

expand

lo g_{11} (\frac{x + y}{x ^{2} y})

lo g_{11} (x + y) - 2 lo g_{11} (x) - lo g_{11} (y)

Solution steps

lo g_{11} (\frac{x + y}{x ^{2} y})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{11} (\frac{x + y}{x ^{2} y}) = lo g_{11} (x + y) - lo g_{11} (x^{2} y)

= lo g_{11} (x + y) - lo g_{11} (x^{2} y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{11} (x^{2} y) = lo g_{11} (x^{2}) + lo g_{11} (y)

= lo g_{11} (x + y) - (lo g_{11} (x^{2}) + lo g_{11} (y))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{11} (x^{2}) = 2 lo g_{11} (x)

= lo g_{11} (x + y) - (2 lo g_{11} (x) + lo g_{11} (y))

- (2 lo g_{11} (x) + lo g_{11} (y)) : - 2 lo g_{11} (x) - lo g_{11} (y)

= lo g_{11} (x + y) - 2 lo g_{11} (x) - lo g_{11} (y)

ln (\frac{( 2 ^{(- 2)} )}{( 3 ^{(2)} 5 ^{(4)} )})

\frac{1}{4} ln (2 + e^{3 x}) - \frac{5}{12} ln (2) - 15 \frac{x}{12} + c

- lo g_{10} (0.1 M)

x + 4 lo g_{5} (y) - 2 lo g_{5} (z)

- \cdot ln (\frac{v _{1}}{v _{4}})

What is expand log_{11}((sqrt(x+y))/(x^2y)) ?
The solution to expand log_{11}((sqrt(x+y))/(x^2y)) is log_{11}(sqrt(x+y))-2log_{11}(x)-log_{11}(y)