What is log_{10}((xy)/(x/y)x^2y) ?

The solution to log_{10}((xy)/(x/y)x^2y) is 2log_{10}(x)+3log_{10}(y)

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simplify log_{10}((xy)/(x/y)x^2y)

simplify

lo g_{10} (\frac{x y}{\frac{x}{y}} x^{2} y)

2 lo g_{10} (x) + 3 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x y}{\frac{x}{y}} x^{2} y)

Apply log rule:

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

lo g_{10} (\frac{x y}{\frac{x}{y}} x^{2} y) = lo g_{10} (\frac{x y}{\frac{x}{y}}) + lo g_{10} (x^{2}) + lo g_{10} (y)

= lo g_{10} (\frac{x y}{\frac{x}{y}}) + lo g_{10} (x^{2}) + lo g_{10} (y)

Apply log rule:

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

lo g_{10} (x^{2}) = 2 lo g_{10} (x)

= lo g_{10} (\frac{x y}{\frac{x}{y}}) + 2 lo g_{10} (x) + lo g_{10} (y)

Apply log rule:

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

lo g_{10} (\frac{x y}{\frac{x}{y}}) = lo g_{10} (x y) - lo g_{10} (\frac{x}{y})

= lo g_{10} (x y) - lo g_{10} (\frac{x}{y}) + 2 lo g_{10} (x) + lo g_{10} (y)

Apply log rule:

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

lo g_{10} (\frac{x}{y}) = lo g_{10} (x) - lo g_{10} (y)

= lo g_{10} (x y) - (lo g_{10} (x) - lo g_{10} (y)) + 2 lo g_{10} (x) + lo g_{10} (y)

Apply log rule:

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

lo g_{10} (x y) = lo g_{10} (x) + lo g_{10} (y)

= lo g_{10} (x) + lo g_{10} (y) - (lo g_{10} (x) - lo g_{10} (y)) + 2 lo g_{10} (x) + lo g_{10} (y)

Simplify

lo g_{10} (x) + lo g_{10} (y) - (lo g_{10} (x) - lo g_{10} (y)) + 2 lo g_{10} (x) + lo g_{10} (y) : 3 lo g_{10} (x) - (lo g_{10} (x) - lo g_{10} (y)) + 2 lo g_{10} (y)

- (lo g_{10} (x) - lo g_{10} (y)) : - lo g_{10} (x) + lo g_{10} (y)

= 3 lo g_{10} (x) - lo g_{10} (x) + lo g_{10} (y) + 2 lo g_{10} (y)

Simplify

3 lo g_{10} (x) - lo g_{10} (x) + lo g_{10} (y) + 2 lo g_{10} (y) : 2 lo g_{10} (x) + 3 lo g_{10} (y)

= 2 lo g_{10} (x) + 3 lo g_{10} (y)

ln (\frac{1}{θ ^{n}} x^{\frac{1}{θ} - 1})

lo g_{5} ((5^{i})^{2})

ln (\frac{cos ^{3} ( 2 x ) sin ^{3} ( 2 x )}{e ^{x^{2} + 1}})

4 lo g_{w} ((\frac{x}{1296})^{2}) - \frac{1}{3} lo g_{w} (2 x + 8)

\frac{1}{2} lo g_{b} (0.35) - \frac{1}{3} lo g_{b} (0.85)

What is log_{10}((xy)/(x/y)x^2y) ?
The solution to log_{10}((xy)/(x/y)x^2y) is 2log_{10}(x)+3log_{10}(y)