15^{3x-2}=13^{3x-2}

Lösung

1 5^{3 x - 2} = 1 3^{3 x - 2}

x = \frac{- 2 ln ( 13 ) + 2 ln ( 15 )}{3 ( - ln ( 13 ) + ln ( 15 ) )}

Dezimale

x = 0.66666 \dots

Schritte zur Lösung

1 5^{3 x - 2} = 1 3^{3 x - 2}

Wende Exponentenregel an

(3 x - 2) ln (15) = (3 x - 2) ln (13)

Löse

(3 x - 2) ln (15) = (3 x - 2) ln (13) : x = \frac{- 2 ln ( 13 ) + 2 ln ( 15 )}{3 ( - ln ( 13 ) + ln ( 15 ) )}

x = \frac{- 2 ln ( 13 ) + 2 ln ( 15 )}{3 ( - ln ( 13 ) + ln ( 15 ) )}

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

3^{2 x + 1} = 2 7^{x}

2^{x} = 100000

2^{x^{2} - 5 x} = 4^{x - 5}

0. 8^{x} = 0.05