5^{(12)/(t^2)}=18

Lösung

5^{\frac{12}{t ^{2}}} = 18

t = \frac{2 \cdot 3 ^{\frac{1}{2}} ln ^{\frac{1}{2}} ( 5 )}{ln ^{\frac{1}{2}} ( 18 )}, t = - \frac{2 \cdot 3 ^{\frac{1}{2}} ln ^{\frac{1}{2}} ( 5 )}{ln ^{\frac{1}{2}} ( 18 )}

Dezimale

t = 2.58494 \dots, t = - 2.58494 \dots

Schritte zur Lösung

5^{\frac{12}{t ^{2}}} = 18

Wende Exponentenregel an

\frac{12}{t ^{2}} ln (5) = ln (18)

Löse

\frac{12}{t ^{2}} ln (5) = ln (18) : t = \frac{2 \cdot 3 ^{\frac{1}{2}} ln ^{\frac{1}{2}} ( 5 )}{ln ^{\frac{1}{2}} ( 18 )}, t = - \frac{2 \cdot 3 ^{\frac{1}{2}} ln ^{\frac{1}{2}} ( 5 )}{ln ^{\frac{1}{2}} ( 18 )}

t = \frac{2 \cdot 3 ^{\frac{1}{2}} ln ^{\frac{1}{2}} ( 5 )}{ln ^{\frac{1}{2}} ( 18 )}, t = - \frac{2 \cdot 3 ^{\frac{1}{2}} ln ^{\frac{1}{2}} ( 5 )}{ln ^{\frac{1}{2}} ( 18 )}

5^{x - 1} - 4^{x} = 0

2^{2 x - 1} = 8^{x}

(5^{x})^{3} = 25.12 5^{x}

e^{2 - 4 x} = 4

e^{2 - 4 x} = 6