a^x=kb^x

Lösung

a^{x} = k b^{x}

x = \frac{ln ( k )}{ln ( a ) - ln ( b )}

Schritte zur Lösung

a^{x} = k b^{x}

Wende Exponentenregel an

x ln (a) = ln (k) + x ln (b)

Löse

x ln (a) = ln (k) + x ln (b) : x = \frac{ln ( k )}{ln ( a ) - ln ( b )}

x = \frac{ln ( k )}{ln ( a ) - ln ( b )}

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

so l v e f or k, k (x) = x^{6} e^{5 x}

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

1 0^{l o g_{10} (x^{2})} = 4

3^{x + 4} = 5^{x + 2}