(2x+3)ln(5)=60(ln(x))

Lösung

(2 x + 3) ln (5) = 60 (ln (x))

x = - \frac{30 W _{- 1} ( - \frac{e ^{\frac{l n ( 5 )}{20}} l n ( 5 )}{30} )}{ln ( 5 )}, x = - \frac{30 W _{0} ( - \frac{e ^{\frac{l n ( 5 )}{20}} l n ( 5 )}{30} )}{ln ( 5 )}

Dezimale

x = 80.23612 \dots, x = 1.15295 \dots

Schritte zur Lösung

(2 x + 3) ln (5) = 60 (ln (x))

Tausche die Seiten

60 ln (x) = (2 x + 3) ln (5)

Teile beide Seiten durch

60

ln (x) = \frac{( 2 x + 3 ) ln ( 5 )}{60}

Wenn

f (x) = g (x),

dann

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

e^{l n (x)} = e^{\frac{( 2 x + 3 ) l n ( 5 )}{60}}

Vereinfache

e^{l n (x)} : x

x = e^{\frac{( 2 x + 3 ) l n ( 5 )}{60}}

Löse

x = e^{\frac{( 2 x + 3 ) l n ( 5 )}{60}} : x = - \frac{30 W _{- 1} ( - \frac{e ^{\frac{l n ( 5 )}{20}} l n ( 5 )}{30} )}{ln ( 5 )}, x = - \frac{30 W _{0} ( - \frac{e ^{\frac{l n ( 5 )}{20}} l n ( 5 )}{30} )}{ln ( 5 )}

x = - \frac{30 W _{- 1} ( - \frac{e ^{\frac{l n ( 5 )}{20}} l n ( 5 )}{30} )}{ln ( 5 )}, x = - \frac{30 W _{0} ( - \frac{e ^{\frac{l n ( 5 )}{20}} l n ( 5 )}{30} )}{ln ( 5 )}

Überprüfe die Lösungen:

x = - \frac{30 W _{- 1} ( - \frac{e ^{\frac{l n ( 5 )}{20}} l n ( 5 )}{30} )}{ln ( 5 )}

Wahr

, x = - \frac{30 W _{0} ( - \frac{e ^{\frac{l n ( 5 )}{20}} l n ( 5 )}{30} )}{ln ( 5 )}

Wahr

Die Lösungen sind

x = - \frac{30 W _{- 1} ( - \frac{e ^{\frac{l n ( 5 )}{20}} l n ( 5 )}{30} )}{ln ( 5 )}, x = - \frac{30 W _{0} ( - \frac{e ^{\frac{l n ( 5 )}{20}} l n ( 5 )}{30} )}{ln ( 5 )}

lo g_{2} (x) + 3 = lo g_{2} (x - 7)

lo g_{7 x} (1) = x

so l v e f or x, 0.8 ln (y) = ln (x)

lo g_{4} (\frac{x + 1}{2 x - 1}) = 0

lo g_{10} (2 x) + 1 = 0