What is 2log_{10}(x)-log_{10}(1/x)-log_{10}(y) ?

The solution to 2log_{10}(x)-log_{10}(1/x)-log_{10}(y) is 3log_{10}(x)-log_{10}(y)

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simplify 2log_{10}(x)-log_{10}(1/x)-log_{10}(y)

simplify

2 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)

3 lo g_{10} (x) - lo g_{10} (y)

Solution steps

2 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)

Simplify

lo g_{10} (\frac{1}{x}) : - lo g_{10} (x)

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

Apply rule:

a - (- b) = a + b

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

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

Add similar elements:

2 lo g_{10} (x) + lo g_{10} (x) = 3 lo g_{10} (x)

= 3 lo g_{10} (x) - lo g_{10} (y)

lo g_{10} (\frac{2 x ^{3} + 4}{5 x ^{3} - x})

33.33 (1) ln (\frac{1100}{1400}) - 0.287 ln (\frac{5}{20})

ln (7) + 2 ln (5)

lo g_{7} (2 x) + lo g_{7} (2) + 5

lo g_{5} (6) + lo g_{5} (x)

What is 2log_{10}(x)-log_{10}(1/x)-log_{10}(y) ?
The solution to 2log_{10}(x)-log_{10}(1/x)-log_{10}(y) is 3log_{10}(x)-log_{10}(y)