English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

vereinfachen 3ln(x^2)+5ln(y)-2ln(a)+4ln(b^3)-3ln(c)+2

Lösung

vereinfachen

3 ln (x^{2}) + 5 ln (y) - 2 ln (a) + 4 ln (b^{3}) - 3 ln (c) + 2

ln (\frac{b ^{12} x ^{6} y ^{5}}{a ^{2} c ^{3}}) + 2

Schritte zur Lösung

3 ln (x^{2}) + 5 ln (y) - 2 ln (a) + 4 ln (b^{3}) - 3 ln (c) + 2

Wende die log Regel an:

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

3 ln (x^{2}) = ln ((x^{2})^{3})

= ln ((x^{2})^{3}) + 5 ln (y) - 2 ln (a) + 4 ln (b^{3}) - 3 ln (c) + 2

Wende die log Regel an:

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

5 ln (y) = ln (y^{5})

= ln ((x^{2})^{3}) + ln (y^{5}) - 2 ln (a) + 4 ln (b^{3}) - 3 ln (c) + 2

Wende die log Regel an:

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

ln ((x^{2})^{3}) + ln (y^{5}) = ln (y^{5} (x^{2})^{3})

= ln (y^{5} (x^{2})^{3}) - 2 ln (a) + 4 ln (b^{3}) - 3 ln (c) + 2

(x^{2})^{3} = x^{6}

= ln (x^{6} y^{5}) - 2 ln (a) + 4 ln (b^{3}) - 3 ln (c) + 2

Wende die log Regel an:

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

2 ln (a) = ln (a^{2})

= ln (x^{6} y^{5}) - ln (a^{2}) + 4 ln (b^{3}) - 3 ln (c) + 2

Wende die log Regel an:

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

ln (x^{6} y^{5}) - ln (a^{2}) = ln (\frac{x ^{6} y ^{5}}{a ^{2}})

= ln (\frac{x ^{6} y ^{5}}{a ^{2}}) + 4 ln (b^{3}) - 3 ln (c) + 2

Wende die log Regel an:

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

4 ln (b^{3}) = ln ((b^{3})^{4})

= ln (\frac{x ^{6} y ^{5}}{a ^{2}}) + ln ((b^{3})^{4}) - 3 ln (c) + 2

Wende die log Regel an:

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

ln (\frac{x ^{6} y ^{5}}{a ^{2}}) + ln ((b^{3})^{4}) = ln (\frac{x ^{6} y ^{5}}{a ^{2}} (b^{3})^{4})

= ln (\frac{x ^{6} y ^{5}}{a ^{2}} (b^{3})^{4}) - 3 ln (c) + 2

Vereinfache

\frac{x ^{6} y ^{5}}{a ^{2}} (b^{3})^{4} : \frac{b ^{12} x ^{6} y ^{5}}{a ^{2}}

= ln (\frac{b ^{12} x ^{6} y ^{5}}{a ^{2}}) - 3 ln (c) + 2

Wende die log Regel an:

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

3 ln (c) = ln (c^{3})

= ln (\frac{b ^{12} x ^{6} y ^{5}}{a ^{2}}) - ln (c^{3}) + 2

Wende die log Regel an:

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

ln (\frac{b ^{12} x ^{6} y ^{5}}{a ^{2}}) - ln (c^{3}) = ln (\frac{\frac{b ^{12} x ^{6} y ^{5}}{a ^{2}}}{c ^{3}})

= ln (\frac{\frac{b ^{12} x ^{6} y ^{5}}{a ^{2}}}{c ^{3}}) + 2

Wende Bruchregel an:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= ln (\frac{b ^{12} x ^{6} y ^{5}}{a ^{2} c ^{3}}) + 2

s im pl i f y \frac{125 \cdot 1.5 \cdot 1 0 ^{6}}{200 \cdot 25 \cdot 50} \cdot ln (\frac{150}{100})

s im pl i f y - \frac{1}{4} ln ∣ x + 2 ∣ + \frac{1}{4} ln ∣ x - 2 ∣

s im pl i f y ln (2) + 2 (ln (2 + 2 - 1)) + ln (3)

s im pl i f y \frac{1}{3} lo g_{3} (7) - lo g_{3} (2)

s im pl i f y ln (\frac{( x + e ^{x} )}{( x ^{2} - 2 )})