What is log_{10}(2x+2)+log_{10}(x)-log_{10}(12) ?

The solution to log_{10}(2x+2)+log_{10}(x)-log_{10}(12) is log_{10}(((x+1)x)/6)

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simplify log_{10}(2x+2)+log_{10}(x)-log_{10}(12)

simplify

lo g_{10} (2 x + 2) + lo g_{10} (x) - lo g_{10} (12)

lo g_{10} (\frac{( x + 1 ) x}{6})

Solution steps

lo g_{10} (2 x + 2) + lo g_{10} (x) - lo g_{10} (12)

Apply log rule:

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

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

= lo g_{10} ((2 x + 2) x) - lo g_{10} (12)

Apply log rule:

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

lo g_{10} ((2 x + 2) x) - lo g_{10} (12) = lo g_{10} (\frac{( 2 x + 2 ) x}{12})

= lo g_{10} (\frac{( 2 x + 2 ) x}{12})

Simplify

\frac{( 2 x + 2 ) x}{12} : \frac{( x + 1 ) x}{6}

= lo g_{10} (\frac{( x + 1 ) x}{6})

ln (\frac{e ^{4}}{5})

ln (x y^{2})

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

- ln (\frac{x}{y})

ln (x^{3}) - ln (x)

What is log_{10}(2x+2)+log_{10}(x)-log_{10}(12) ?
The solution to log_{10}(2x+2)+log_{10}(x)-log_{10}(12) is log_{10}(((x+1)x)/6)