What is log_{10}((x+y)^3)-log_{10}(x+y) ?

The solution to log_{10}((x+y)^3)-log_{10}(x+y) is 2log_{10}(x+y)

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simplify log_{10}((x+y)^3)-log_{10}(x+y)

simplify

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

2 lo g_{10} (x + y)

Solution steps

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{10} ((x + y)^{3}) = 3 lo g_{10} (x + y)

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

Add similar elements:

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

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

lo g_{4} (x^{2} - 1) - 5 lo g_{4} (x + 1)

lo g_{3} (\frac{100}{27 x})

ln (\frac{4 e ^{6}}{7 y})

lo g_{7} (x) - lo g_{7} (x^{2})

ln (\frac{x}{b})

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