What is log_{10}(10x)+log_{10}(20y)-log_{10}(10) ?

The solution to log_{10}(10x)+log_{10}(20y)-log_{10}(10) is log_{10}(2xy)+1

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simplify log_{10}(10x)+log_{10}(20y)-log_{10}(10)

simplify

lo g_{10} (10 x) + lo g_{10} (20 y) - lo g_{10} (10)

lo g_{10} (2 x y) + 1

Solution steps

lo g_{10} (10 x) + lo g_{10} (20 y) - lo g_{10} (10)

Apply log rule:

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

lo g_{10} (10 x) + lo g_{10} (20 y) = lo g_{10} (10 x \cdot 20 y)

= lo g_{10} (10 x \cdot 20 y) - lo g_{10} (10)

Apply log rule:

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

lo g_{10} (10 x \cdot 20 y) - lo g_{10} (10) = lo g_{10} (\frac{10 x \cdot 20 y}{10})

= lo g_{10} (\frac{10 x \cdot 20 y}{10})

Simplify

\frac{10 x \cdot 20 y}{10} : x \cdot 20 y

= lo g_{10} (x \cdot 20 y)

Apply log rule:

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

lo g_{10} (x \cdot 20 y) = lo g_{10} (x) + lo g_{10} (20) + lo g_{10} (y)

= lo g_{10} (x) + lo g_{10} (20) + lo g_{10} (y)

lo g_{10} (20) = 1 + lo g_{10} (2)

= lo g_{10} (x) + 1 + lo g_{10} (2) + lo g_{10} (y)

Simplify

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

= lo g_{10} (x \cdot 2 y) + 1

= lo g_{10} (2 x y) + 1

ln (\frac{23}{20})

ln (c \frac{x ^{a}}{z ^{b}})

\frac{1}{2} ln (\frac{120}{500})

ln (5) + \frac{1}{3} ln (8)

5 lo g_{2} (x) + 5 lo g_{2} (y)

What is log_{10}(10x)+log_{10}(20y)-log_{10}(10) ?
The solution to log_{10}(10x)+log_{10}(20y)-log_{10}(10) is log_{10}(2xy)+1