vereinfachen 1/2 log_{10}(x+3)+1/2 log_{10}(2x-1)

Lösung

vereinfachen

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

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

Schritte zur Lösung

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

Wende die log Regel an:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} lo g_{10} (x + 3) = lo g_{10} ((x + 3)^{\frac{1}{2}})

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

Wende die log Regel an:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} lo g_{10} (2 x - 1) = lo g_{10} ((2 x - 1)^{\frac{1}{2}})

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

Wende die log Regel an:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

j o in \frac{ln ( \frac{69}{97} )}{2 ln ( 2 )}

j o in \frac{1}{5} lo g_{3} (10)

s im pl i f y - \frac{1}{16} lo g_{e} (\frac{1}{16}) - \frac{15}{16} lo g_{e} (\frac{15}{16})

s im pl i f y ln (2 \cdot e^{- 10 k})

s im pl i f y \frac{6 ln ( 7 ) - 2 ln ( 5 )}{- ln ( 5 ) - 5 ln ( 7 )}