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vereinfachen 3ln(5)+1/2 ln(9)-3ln(3)-5ln(25)

Lösung

vereinfachen

3 ln (5) + \frac{1}{2} ln (9) - 3 ln (3) - 5 ln (25)

- ln (703125)

Dezimale

- 13.46328 \dots

Schritte zur Lösung

3 ln (5) + \frac{1}{2} ln (9) - 3 ln (3) - 5 ln (25)

Wende die log Regel an:

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

3 ln (5) = ln (5^{3})

= ln (5^{3}) + \frac{1}{2} ln (9) - 3 ln (3) - 5 ln (25)

Wende die log Regel an:

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

\frac{1}{2} ln (9) = ln (9^{\frac{1}{2}})

= ln (5^{3}) + ln (9^{\frac{1}{2}}) - 3 ln (3) - 5 ln (25)

Wende die log Regel an:

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

ln (5^{3}) + ln (9^{\frac{1}{2}}) = ln (5^{3} \cdot 9^{\frac{1}{2}})

= ln (5^{3} \cdot 9^{\frac{1}{2}}) - 3 ln (3) - 5 ln (25)

5^{3} \cdot 9^{\frac{1}{2}} = 375

= ln (375) - 3 ln (3) - 5 ln (25)

Wende die log Regel an:

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

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

= ln (375) - ln (3^{3}) - 5 ln (25)

Wende die log Regel an:

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

ln (375) - ln (3^{3}) = ln (\frac{375}{3 ^{3}})

= ln (\frac{375}{3 ^{3}}) - 5 ln (25)

\frac{375}{3 ^{3}} = \frac{125}{9}

= ln (\frac{125}{9}) - 5 ln (25)

Wende die log Regel an:

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

5 ln (25) = ln (2 5^{5})

= ln (\frac{125}{9}) - ln (2 5^{5})

Wende die log Regel an:

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

ln (\frac{125}{9}) - ln (2 5^{5}) = ln (\frac{\frac{125}{9}}{2 5 ^{5}})

= ln (\frac{\frac{125}{9}}{2 5 ^{5}})

\frac{\frac{125}{9}}{2 5 ^{5}} = \frac{1}{703125}

= ln (\frac{1}{703125})

Wende die log Regel an:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (703125)

s im pl i f y lo g_{10} (a) + 2 lo g_{10} (c)

s im pl i f y ln (2 sinh (\frac{h w}{2 k x}))

s im pl i f y 8 ln ∣ 8 x + 1 ∣ - 8 ln ∣ x + 1 ∣

s im pl i f y ln (\frac{k}{n}) - e^{a t + c}

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