Question

1) Sa se rezolve ecuatiile:
a) log2 x= log2 (3x-1)
b) log3 (x la 2-8x=log3 9
c) lg(x la 2-4x+2)=lg(x-2)

2) Sa se rezolve ecuatiile:
a) log4 x=2
b) lg(x-1)=-1
c) log1/4(7x+1)=log9 27

Answer 1

$1a) log_{2}x= log_{2}(3x-1);DVA:x\ \textgreater \ \frac{1}{3} \\ x=3x-1 \\ -2x=-1 \\ x= \frac{1}{2} \\ b) DVA:x :apartie(-infinit;0)u(8;+infinit) \\ x^{2} -8x=9 \\ x^{2} -8x-9=0 \\ x=-1;x=9 \\ c)DVA:x\ \textgreater \ 2 \\ x^{2} -4x+2=x-2 \\ x^{2} -5x+4=0 \\ x \neq 1;x=4 \\ 2a)x= 4^{2} =16 \\ b)x-1= 10^{-1} \\ x= \frac{1}{10}+1 \\ x= \frac{11}{10} \\ c)7x+1=( \frac{1}{4} ^{ \frac{3}{2} } ) \\ 7x+1= \frac{1}{8} \\ x=- \frac{7}{8}* \frac{1}{7} \\ x=- \frac{1}{8}$