What is log_{10}(100xy) ?

The solution to log_{10}(100xy) is 2+log_{10}(x)+log_{10}(y)

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simplify log_{10}(100xy)

simplify

lo g_{10} (100 x y)

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

Solution steps

lo g_{10} (100 x y)

Factor the number:

100 = 1 0^{2}

= lo g_{10} (1 0^{2} x y)

Apply log rule:

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

lo g_{10} (1 0^{2} x y) = lo g_{10} (1 0^{2}) + lo g_{10} (x y)

= lo g_{10} (1 0^{2}) + lo g_{10} (x y)

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{10} (1 0^{2}) = 2

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

Apply log rule:

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

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

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

Apply rule:

a + (b + c) = a + b + c

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

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

lo g_{2} (3 x) + 1

ln^{2} (\frac{1}{e}) + (- \frac{1}{2}) - ln^{2} (- 1)

lo g_{10} (y^{7} x z^{3})

3 ln (x) - \frac{1}{2} ln (3 x + 1) + 5 ln (x - 1) - ln (x + 5)

lo g_{10} (\frac{x}{x + 1})

What is log_{10}(100xy) ?
The solution to log_{10}(100xy) is 2+log_{10}(x)+log_{10}(y)