vereinfachen log_{10}(((x+1)(x-8))/((x-1)(x+8)))

Lösung

vereinfachen

lo g_{10} (\frac{( x + 1 ) ( x - 8 )}{( x - 1 ) ( x + 8 )})

lo g_{10} (x + 1) + lo g_{10} (x - 8) - lo g_{10} (x - 1) - lo g_{10} (x + 8)

Schritte zur Lösung

lo g_{10} (\frac{( x + 1 ) ( x - 8 )}{( x - 1 ) ( x + 8 )})

Wende die log Regel an:

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

lo g_{10} (\frac{( x + 1 ) ( x - 8 )}{( x - 1 ) ( x + 8 )}) = lo g_{10} ((x + 1) (x - 8)) - lo g_{10} ((x - 1) (x + 8))

= lo g_{10} ((x + 1) (x - 8)) - lo g_{10} ((x - 1) (x + 8))

lo g_{10} ((x + 1) (x - 8)) = lo g_{10} (x + 1) + lo g_{10} (x - 8)

lo g_{10} ((x - 1) (x + 8)) = lo g_{10} (x - 1) + lo g_{10} (x + 8)

= lo g_{10} (x + 1) + lo g_{10} (x - 8) - (lo g_{10} (x - 1) + lo g_{10} (x + 8))

Wende das Distributivgesetz an:

- (a + b) = - a - b

- (lo g_{10} (x - 1) + lo g_{10} (x + 8)) = - lo g_{10} (x - 1) - lo g_{10} (x + 8)

= lo g_{10} (x + 1) + lo g_{10} (x - 8) - lo g_{10} (x - 1) - lo g_{10} (x + 8)

\int 3^{x} + \frac{2}{x} d x

\frac{\partial}{\partial x} (e^{8 x y})

\frac{d}{d x} (x^{k})

x \to \infty lim (- \frac{1}{3})

\frac{d}{d x} (\frac{( x ^{2} )}{2 + x})