5000*log_{10}(n)=n

Lösung

5000 \cdot lo g_{10} (n) = n

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

Dezimale

n = 21680.32937 \dots, n = 1.00046 \dots

Schritte zur Lösung

5000 lo g_{10} (n) = n

Teile beide Seiten durch

5000

lo g_{10} (n) = \frac{n}{5000}

Wenn

f (x) = g (x),

dann

a^{f (x)} = a^{g (x)}

1 0^{l o g_{10} (n)} = 1 0^{\frac{n}{5000}}

Vereinfache

1 0^{l o g_{10} (n)} : n

n = 1 0^{\frac{n}{5000}}

Löse

n = 1 0^{\frac{n}{5000}} : n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

Überprüfe die Lösungen:

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

Wahr

, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

Wahr

Die Lösungen sind

n = - \frac{5000 W _{- 1} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}, n = - \frac{5000 W _{0} ( - \frac{l n ( 10 )}{5000} )}{ln ( 10 )}

6.5 = - lo g_{10} (x)

2 lo g_{2} (y) + lo g_{4} (y) = 9

x - 1 = lo g_{2} (3^{x})

so l v e f or y, lo g_{5} (y) = x

2 lo g_{3} (4 x + 1) = 4