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

The solution to log_{10}(a+b)-log_{10}(a)-log_{10}(b) is log_{10}((a+b)/(ab))

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

simplify

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

lo g_{10} (\frac{a + b}{ab})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= lo g_{10} (\frac{\frac{a + b}{a}}{b})

Simplify

\frac{\frac{a + b}{a}}{b} : \frac{a + b}{ab}

= lo g_{10} (\frac{a + b}{ab})

lo g_{10} (\frac{k}{r})

4 lo g_{10} (a) - \frac{1}{2} lo g_{10} (b) + lo g_{10} (c)

ln (e^{19} x^{20})

lo g_{10} (\frac{x ^{3} ( x + 3 )}{( x - 1 ) x + 5})

\frac{2 ln ( 2 )}{ln ( 2 ) - 2 ln ( 3 )}

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