vereinfachen 2x+ln(cos(3x))-1/2 ln(x-4)

Lösung

vereinfachen

2 x + ln (cos (3 x)) - \frac{1}{2} ln (x - 4)

2 x + ln (\frac{cos ( 3 x ) x - 4}{x - 4})

Schritte zur Lösung

2 x + ln (cos (3 x)) - \frac{1}{2} ln (x - 4)

Wende die log Regel an:

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

\frac{1}{2} ln (x - 4) = ln ((x - 4)^{\frac{1}{2}})

= 2 x + ln (cos (3 x)) - ln ((x - 4)^{\frac{1}{2}})

Wende die log Regel an:

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

ln (cos (3 x)) - ln ((x - 4)^{\frac{1}{2}}) = ln (\frac{cos ( 3 x )}{( x - 4 ) ^{\frac{1}{2}}})

= 2 x + ln (\frac{cos ( 3 x )}{( x - 4 ) ^{\frac{1}{2}}})

Vereinfache

\frac{cos ( 3 x )}{( x - 4 ) ^{\frac{1}{2}}} : \frac{cos ( 3 x ) x - 4}{x - 4}

= 2 x + ln (\frac{cos ( 3 x ) x - 4}{x - 4})

j o in - \frac{ln ( \frac{5}{22} )}{2 ln ( \frac{110}{7} )}

s im pl i f y ln (100 e^{x})

s im pl i f y - ln (\frac{1}{0.99})

s im pl i f y ln (\frac{- 1 \cdot 3 ^{n}}{2 ^{n} b ^{n}})

j o in \frac{1 3 ^{\frac{2 l n ( 2 )}{l n ( 13 )}} + 10}{6}