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Beliebt Algebra >

3log_{10}(2x+6)=x+2

Lösung

3 lo g_{10} (2 x + 6) = x + 2

Lösung

x = - \frac{3 W _{- 1} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 3, x = - \frac{3 W _{0} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 3

+1

Dezimale

x = 0.55596 \dots, x = - 2.71008 \dots

Schritte zur Lösung

3 lo g_{10} (2 x + 6) = x + 2

Teile beide Seiten durch

3

lo g_{10} (2 x + 6) = \frac{x + 2}{3}

Wenn

f (x) = g (x),

dann

a^{f (x)} = a^{g (x)}

1 0^{l o g_{10} (2 x + 6)} = 1 0^{\frac{x + 2}{3}}

Vereinfache

1 0^{l o g_{10} (2 x + 6)} : 2 x + 6

2 x + 6 = 1 0^{\frac{x + 2}{3}}

Löse

2 x + 6 = 1 0^{\frac{x + 2}{3}} : x = - \frac{3 W _{- 1} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 3, x = - \frac{3 W _{0} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 3

x = - \frac{3 W _{- 1} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 3, x = - \frac{3 W _{0} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 3

Überprüfe die Lösungen:

x = - \frac{3 W _{- 1} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 3

Wahr

, x = - \frac{3 W _{0} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 3

Wahr

Die Lösungen sind

x = - \frac{3 W _{- 1} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 3, x = - \frac{3 W _{0} ( - \frac{l n ( 10 )}{6 e ^{\frac{l n ( 10 )}{3}}} )}{ln ( 10 )} - 3

Graph

Beliebte Beispiele

13=-log_{10}(x)

13 = - lo g_{10} (x)

ln(esqrt(x^3))=2

ln (e x^{3}) = 2

lo g_{3} (x - 2) = 0

solvefor x,36=4ln(sqrt(x)-1)

so l v e f or x, 36 = 4 ln (x - 1)

solvefor x,ln(y)=-2ln(x)

so l v e f or x, ln (y) = - 2 ln (x)