log_{10}(x^{64})=-3

Lösung

lo g_{10} (x^{64}) = - 3

x = \frac{1}{1 0 ^{\frac{3}{64}}}, x = - \frac{1}{1 0 ^{\frac{3}{64}}}

Dezimale

x = 0.89768 \dots, x = - 0.89768 \dots

Schritte zur Lösung

lo g_{10} (x^{64}) = - 3

Wende Exponentenregel an:

a^{2 \cdot n} = (a^{2})^{n}

x^{64} = (x^{2})^{32}

lo g_{10} ((x^{2})^{32}) = - 3

Wende die log Regel an

x^{2} = \frac{1}{1 0 ^{\frac{3}{32}}}

Löse

x^{2} = \frac{1}{1 0 ^{\frac{3}{32}}} : x = \frac{1}{1 0 ^{\frac{3}{64}}}, x = - \frac{1}{1 0 ^{\frac{3}{64}}}

x = \frac{1}{1 0 ^{\frac{3}{64}}}, x = - \frac{1}{1 0 ^{\frac{3}{64}}}

Überprüfe die Lösungen:

x = \frac{1}{1 0 ^{\frac{3}{64}}}

Wahr

, x = - \frac{1}{1 0 ^{\frac{3}{64}}}

Wahr

Die Lösungen sind

x = \frac{1}{1 0 ^{\frac{3}{64}}}, x = - \frac{1}{1 0 ^{\frac{3}{64}}}

lo g_{6} (7 x + 1) = 2

lo g_{5} (10) = lo g_{10} (x)

lo g_{a} (a^{n}) = n

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

5 = 10 lo g_{10} (x)