3^{x+2}=10^x

Lösung

3^{x + 2} = 1 0^{x}

x = \frac{2 ln ( 3 )}{ln ( 10 ) - ln ( 3 )}

Dezimale

x = 1.82497 \dots

Schritte zur Lösung

3^{x + 2} = 1 0^{x}

Wende Exponentenregel an

(x + 2) ln (3) = x ln (10)

Löse

(x + 2) ln (3) = x ln (10) : x = \frac{2 ln ( 3 )}{ln ( 10 ) - ln ( 3 )}

x = \frac{2 ln ( 3 )}{ln ( 10 ) - ln ( 3 )}

2^{(2 x + 3)} = 3^{3 x}

5^{x} = 3125

3^{2 x + 1} - 10 (3^{x}) + 3 = 0

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

3^{x} = - 2