x^{log_{10}(4x)}-17=239

Lösung

x^{l o g_{10} (4 x)} - 17 = 239

x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) + 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}, x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) - 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

Dezimale

x = 19.04355 \dots, x = 0.01312 \dots

Schritte zur Lösung

x^{l o g_{10} (4 x)} - 17 = 239

Wende Exponentenregel an

lo g_{10} (4 x) ln (x) = ln (256)

Löse

lo g_{10} (4 x) ln (x) = ln (256) : x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) + 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}, x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) - 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) + 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}, x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) - 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

Überprüfe die Lösungen:

x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) + 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

Wahr

, x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) - 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

Wahr

Die Lösungen sind

x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) + 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}, x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) - 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

x e^{x} - 2 = 0

6^{3 x + 1} = 2^{2 x - 3}

10 0^{x} = 1

3^{(x - 4)} = 7

(\frac{1}{4})^{x + 1} = 32