What is log_{10}((a+b)^2)-log_{10}(a+b) ?

The solution to log_{10}((a+b)^2)-log_{10}(a+b) is log_{10}(a+b)

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simplify log_{10}((a+b)^2)-log_{10}(a+b)

simplify

lo g_{10} ((a + b)^{2}) - lo g_{10} (a + b)

lo g_{10} (a + b)

Solution steps

lo g_{10} ((a + b)^{2}) - lo g_{10} (a + b)

Apply log rule

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

lo g_{10} ((a + b)^{2}) = 2 lo g_{10} (a + b)

= 2 lo g_{10} (a + b) - lo g_{10} (a + b)

Add similar elements:

2 lo g_{10} (a + b) - lo g_{10} (a + b) = lo g_{10} (a + b)

= lo g_{10} (a + b)

ln (2 π)

ln (2 x) - ln (x)

lo g_{10} (x) - 2 lo g_{10} (y) + 5 lo g_{10} (z)

lo g_{10} (\frac{2 x + y}{y ^{3}})

lo g_{2} (5) + lo g_{2} (2 x - 3)

What is log_{10}((a+b)^2)-log_{10}(a+b) ?
The solution to log_{10}((a+b)^2)-log_{10}(a+b) is log_{10}(a+b)