What is log_{10}(2x)+log_{10}(50y) ?

The solution to log_{10}(2x)+log_{10}(50y) is 2+log_{10}(xy)

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simplify log_{10}(2x)+log_{10}(50y)

simplify

lo g_{10} (2 x) + lo g_{10} (50 y)

2 + lo g_{10} (x y)

Solution steps

lo g_{10} (2 x) + lo g_{10} (50 y)

Apply log rule:

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

lo g_{10} (2 x) + lo g_{10} (50 y) = lo g_{10} (2 x \cdot 50 y)

= lo g_{10} (2 x \cdot 50 y)

Simplify

2 x \cdot 50 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_{2} (x y)

lo g_{6} (\frac{c}{36})

lo g_{10} (\frac{x ( x + 6 )}{( x + 5 ) ^{6}})

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

2 lo g_{10} (x y)

What is log_{10}(2x)+log_{10}(50y) ?
The solution to log_{10}(2x)+log_{10}(50y) is 2+log_{10}(xy)