What is log_{10}(x)+2log_{10}(6y) ?

The solution to log_{10}(x)+2log_{10}(6y) is log_{10}(36xy^2)

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simplify log_{10}(x)+2log_{10}(6y)

simplify

lo g_{10} (x) + 2 lo g_{10} (6 y)

lo g_{10} (36 x y^{2})

Solution steps

lo g_{10} (x) + 2 lo g_{10} (6 y)

Apply log rule:

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

2 lo g_{10} (6 y) = lo g_{10} ((6 y)^{2})

= lo g_{10} (x) + lo g_{10} ((6 y)^{2})

Apply log rule:

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

lo g_{10} (x) + lo g_{10} ((6 y)^{2}) = lo g_{10} (x (6 y)^{2})

= lo g_{10} (x (6 y)^{2})

Simplify

(6 y)^{2} : 36 y^{2}

= lo g_{10} (x \cdot 36 y^{2})

= lo g_{10} (36 x y^{2})

- 0.1 lo g_{2} (0.1) - 0.9 lo g_{2} (0.9)

lo g_{10} (2) + lo g_{10} (x + 3) - lo g_{10} (x + 5)

ln (\frac{10}{x})

lo g_{2} (\frac{x}{5})

ln (\frac{16}{5})

What is log_{10}(x)+2log_{10}(6y) ?
The solution to log_{10}(x)+2log_{10}(6y) is log_{10}(36xy^2)