Logarithmus Gleichung lösen..

Question

Ermittle jeweils die Definitionsmenge der logarithmischen Gleichung und löse die Gleichung.

-log₄(2x) = 6

2ln(3x -3)) = 1

lg(x + 1) - lg(2) = 2

Answer 1

-log₄(2x) = 6

log₄(2x) = - 6

2x = 4^{- 6}

2x = 1/4096

x = 1/8192

Answer 2

- log(2x)/log(4)=6

- (log(x) +log(2))/log(4) =6

log(8192x)=0

x=1/8192

DB: x>0

2ln(3x -3)) = 1

ln(3x -3)) = 1/2

3x -3 = e^{1/2}

3x  = e^{1/2} +3

x= (e^{1/2} +3)/3

DB x>1

lg(x + 1) - lg(2) = 2

lg((x+1)/(2))=2

(x+1)/(2)=10^{2}

x+1=200

x=199

DB: x> -1