2^{1/2}+2^{1/3}=2^x

Lösung

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

x = \frac{ln ( 2 ^{\frac{1}{2}} + 2 ^{\frac{1}{3}} )}{ln ( 2 )}

Dezimale

x = 1.41907 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

ln (2^{\frac{1}{2}} + 2^{\frac{1}{3}}) = x ln (2)

Löse

ln (2^{\frac{1}{2}} + 2^{\frac{1}{3}}) = x ln (2) : x = \frac{ln ( 2 ^{\frac{1}{2}} + 2 ^{\frac{1}{3}} )}{ln ( 2 )}

x = \frac{ln ( 2 ^{\frac{1}{2}} + 2 ^{\frac{1}{3}} )}{ln ( 2 )}

1.0 8^{x} = 2

(\frac{1}{2})^{x} = 0.26

so l v e f or a, 2^{a - b} = 2016

3^{x} + 3^{x + 2} = 7290

\frac{5}{2 \cdot 2 ^{x} - 2 ^{x} - 2 ^{- 1}} = 16