2^{((n(n+1))/2)}=100

Lösung

2^{(\frac{n ( n + 1 )}{2})} = 100

n = \frac{- ln ( 2 ) + ( ln ^{2} ( 2 ) + 16 ln ( 2 ) ln ( 10 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}, n = \frac{- ln ( 2 ) - ( ln ^{2} ( 2 ) + 16 ln ( 2 ) ln ( 10 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}

Dezimale

n = 3.17936 \dots, n = - 4.17936 \dots

Schritte zur Lösung

2^{(\frac{n ( n + 1 )}{2})} = 100

Wende Exponentenregel an

\frac{n ( n + 1 )}{2} ln (2) = ln (100)

Löse

\frac{n ( n + 1 )}{2} ln (2) = ln (100) : n = \frac{- ln ( 2 ) + ( ln ^{2} ( 2 ) + 16 ln ( 2 ) ln ( 10 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}, n = \frac{- ln ( 2 ) - ( ln ^{2} ( 2 ) + 16 ln ( 2 ) ln ( 10 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}

n = \frac{- ln ( 2 ) + ( ln ^{2} ( 2 ) + 16 ln ( 2 ) ln ( 10 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}, n = \frac{- ln ( 2 ) - ( ln ^{2} ( 2 ) + 16 ln ( 2 ) ln ( 10 ) ) ^{\frac{1}{2}}}{2 ln ( 2 )}

400 = 250 (1 + 0.07)^{t}

\frac{30}{1 + e ^{- x}} = 4

\frac{2 ^{x} - 2}{4} = 1 + 2^{2 - x}

7^{x + 3} = 5

7^{x + 3} = 1