10^{log_{10}(x^2+2x)}=8

Lösung

1 0^{l o g_{10} (x^{2} + 2 x)} = 8

x = \frac{- 2 + 4 + 4 \cdot 1 0 ^{\frac{3 l n ( 2 )}{l n ( 10 )}}}{2}, x = \frac{- 2 - 4 + 4 \cdot 1 0 ^{\frac{3 l n ( 2 )}{l n ( 10 )}}}{2}

Dezimale

x = 2, x = - 4

Schritte zur Lösung

1 0^{l o g_{10} (x^{2} + 2 x)} = 8

Wende Exponentenregel an

lo g_{10} (x^{2} + 2 x) ln (10) = ln (8)

Löse

lo g_{10} (x^{2} + 2 x) ln (10) = ln (8) : x = \frac{- 2 + 4 + 4 \cdot 1 0 ^{\frac{3 l n ( 2 )}{l n ( 10 )}}}{2}, x = \frac{- 2 - 4 + 4 \cdot 1 0 ^{\frac{3 l n ( 2 )}{l n ( 10 )}}}{2}

x = \frac{- 2 + 4 + 4 \cdot 1 0 ^{\frac{3 l n ( 2 )}{l n ( 10 )}}}{2}, x = \frac{- 2 - 4 + 4 \cdot 1 0 ^{\frac{3 l n ( 2 )}{l n ( 10 )}}}{2}

5 \frac{1}{243} = 3^{p}

5^{2 x} + 3 \cdot 5^{x} - 4 = 0

\frac{8 ^{n}}{2 ^{n}} = 16

440 \cdot 1.00 7^{t} = 3383

8^{x - 2} = 8