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

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

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

simplify

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

2 + lo g_{10} (x y)

Solution steps

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

Apply log rule:

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

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

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

Simplify

10 x \cdot 10 y : 100 x y

= lo g_{10} (100 x y)

Apply log rule:

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

lo g_{10} (100 x y) = lo g_{10} (100) + lo g_{10} (x) + lo g_{10} (y)

= lo g_{10} (100) + lo g_{10} (x) + lo g_{10} (y)

lo g_{10} (100) = 2

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

Apply log rule:

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

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

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

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

- 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})

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