x^{log_{5}(x)}=9

Lösung

x^{l o g_{5} (x)} = 9

x = 5^{\frac{2 l n ( 3 )}{l n ( 5 )}}, x = \frac{1}{5 ^{\frac{2 l n ( 3 )}{l n ( 5 )}}}

Dezimale

x = 6.55681 \dots, x = 0.15251 \dots

Schritte zur Lösung

x^{l o g_{5} (x)} = 9

Wende Exponentenregel an

lo g_{5} (x) ln (x) = ln (9)

Löse

lo g_{5} (x) ln (x) = ln (9) : x = 5^{\frac{2 l n ( 3 )}{l n ( 5 )}}, x = \frac{1}{5 ^{\frac{2 l n ( 3 )}{l n ( 5 )}}}

x = 5^{\frac{2 l n ( 3 )}{l n ( 5 )}}, x = \frac{1}{5 ^{\frac{2 l n ( 3 )}{l n ( 5 )}}}

Überprüfe die Lösungen:

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

Wahr

, x = \frac{1}{5 ^{\frac{2 l n ( 3 )}{l n ( 5 )}}}

Wahr

Die Lösungen sind

x = 5^{\frac{2 l n ( 3 )}{l n ( 5 )}}, x = \frac{1}{5 ^{\frac{2 l n ( 3 )}{l n ( 5 )}}}

2^{4 x} = 8^{7 - x}

so l v e f or x, 7^{x} = e^{t}

(\frac{5}{2})^{3 x + 4} = (\frac{2}{5})^{4 x + 10}

9^{x} = - 9

2^{x} = 40