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Beliebt Algebra >

-0.2X+log_{10}(X)=-3.2325

Lösung

- 0.2 X + lo g_{10} (X) = - 3.2325

Lösung

X = - \frac{W _{- 1} ( - \frac{0.2 l n ( 10 )}{1 0 ^{3.2325}} )}{0.2 ln ( 10 )}, X = - \frac{W _{0} ( - \frac{0.2 l n ( 10 )}{1 0 ^{3.2325}} )}{0.2 ln ( 10 )}

+1

Dezimale

X = 22.96812 \dots, X = 0.00058 \dots

Schritte zur Lösung

- 0.2 X + lo g_{10} (X) = - 3.2325

Verschiebe

0.2 X

auf die rechte Seite

lo g_{10} (X) = - 3.2325 + 0.2 X

Wenn

f (x) = g (x),

dann

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

1 0^{l o g_{10} (X)} = 1 0^{- 3.2325 + 0.2 X}

Vereinfache

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

X = 1 0^{- 3.2325 + 0.2 X}

Löse

X = 1 0^{- 3.2325 + 0.2 X} : X = - \frac{W _{- 1} ( - \frac{0.2 l n ( 10 )}{1 0 ^{3.2325}} )}{0.2 ln ( 10 )}, X = - \frac{W _{0} ( - \frac{0.2 l n ( 10 )}{1 0 ^{3.2325}} )}{0.2 ln ( 10 )}

X = - \frac{W _{- 1} ( - \frac{0.2 l n ( 10 )}{1 0 ^{3.2325}} )}{0.2 ln ( 10 )}, X = - \frac{W _{0} ( - \frac{0.2 l n ( 10 )}{1 0 ^{3.2325}} )}{0.2 ln ( 10 )}

Überprüfe die Lösungen:

X = - \frac{W _{- 1} ( - \frac{0.2 l n ( 10 )}{1 0 ^{3.2325}} )}{0.2 ln ( 10 )}

Wahr

, X = - \frac{W _{0} ( - \frac{0.2 l n ( 10 )}{1 0 ^{3.2325}} )}{0.2 ln ( 10 )}

Wahr

Die Lösungen sind

X = - \frac{W _{- 1} ( - \frac{0.2 l n ( 10 )}{1 0 ^{3.2325}} )}{0.2 ln ( 10 )}, X = - \frac{W _{0} ( - \frac{0.2 l n ( 10 )}{1 0 ^{3.2325}} )}{0.2 ln ( 10 )}

Graph

Beliebte Beispiele

log_{10}(X+2(X+5))=1

lo g_{10} (X + 2 (X + 5)) = 1

log_{2}(5)+log_{2}(x-2)=1

lo g_{2} (5) + lo g_{2} (x - 2) = 1

10*log_{10}(x)=3

10 \cdot lo g_{10} (x) = 3

0.35 = ln (y)

- x + ln (x) = c