What is log_{10}((6x^2-24x)/(6x(x+1)(x+3))) ?

The solution to log_{10}((6x^2-24x)/(6x(x+1)(x+3))) is log_{10}(x-4)-log_{10}(x+1)-log_{10}(x+3)

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simplify log_{10}((6x^2-24x)/(6x(x+1)(x+3)))

simplify

lo g_{10} (\frac{6 x ^{2} - 24 x}{6 x ( x + 1 ) ( x + 3 )})

lo g_{10} (x - 4) - lo g_{10} (x + 1) - lo g_{10} (x + 3)

Solution steps

lo g_{10} (\frac{6 x ^{2} - 24 x}{6 x ( x + 1 ) ( x + 3 )})

Simplify

\frac{6 x ^{2} - 24 x}{6 x ( x + 1 ) ( x + 3 )} : \frac{x - 4}{( x + 1 ) ( x + 3 )}

= lo g_{10} (\frac{x - 4}{( x + 1 ) ( x + 3 )})

Apply log rule:

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

lo g_{10} (\frac{x - 4}{( x + 1 ) ( x + 3 )}) = lo g_{10} (x - 4) - lo g_{10} ((x + 1) (x + 3))

= lo g_{10} (x - 4) - lo g_{10} ((x + 1) (x + 3))

Simplify

lo g_{10} ((x + 1) (x + 3)) : lo g_{10} (x + 1) + lo g_{10} (x + 3)

= lo g_{10} (x - 4) - (lo g_{10} (x + 1) + lo g_{10} (x + 3))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (x + 1) + lo g_{10} (x + 3)) = - lo g_{10} (x + 1) - lo g_{10} (x + 3)

= lo g_{10} (x - 4) - lo g_{10} (x + 1) - lo g_{10} (x + 3)

lo g_{g} (\frac{s t ^{6}}{r ^{7}})

lo g_{10} (8) - lo g_{10} (4)

lo g_{10} (y z^{7})

lo g_{4} (6 x^{4})

2 lo g_{8} (9 x) - lo g_{8} (2 x - 5)

What is log_{10}((6x^2-24x)/(6x(x+1)(x+3))) ?
The solution to log_{10}((6x^2-24x)/(6x(x+1)(x+3))) is log_{10}(x-4)-log_{10}(x+1)-log_{10}(x+3)