Question

rezolvati ecuatiile: 

a)3la puterea x+1=81

b)2la puterea x=1 supra 16

c)lg x=-2

d)log(x la a2a +3)=log2(4x) va rog!!

Answer 1

a) $3^{x+1} = 3^{4}$
⇒ x+1=4
   x=3

b) $2^{1}$/16=1/8
c) lg x=-2 ⇒ x=$10^{-2}$=1/100
d) log2 (x2+3)=log2 (4x) ⇒ $x^{2}$+3=4x
$x^{2}$-4x+3=0
delta=16-12=4
$x_{1}$=3
$x_{2}$=1

Answer 2

a)
$3^{x+1} = 81 \\ 3^{x+1} = 3^{4} \\ x+1=4 \\ =>x=4-1 \\ x=3$

b)
$2^{x} = \frac{1}{16} \\ 2^{x} = \frac{1}{ 2^{4}} \\2^{x} =2^{-4} \\ x=-4$

c)
$lg x=-2 \\ 10^{-2} =x \\ x= \frac{1}{10^{2}}= \frac{1}{100} \\ x=0,01$

d)
$log_2( x^{2} +3)=log_2(4x) \\x^{2} +3= 4x \\ x^{2}-4x+3=0 \\ x_1= \frac{4+ \sqrt{16-12} }{2} =\frac{4+ \sqrt{4}}{2}=\frac{4+ 2}{2}= \frac{6}{2}=3 \\x_1= \frac{4- \sqrt{16-12} }{2} =\frac{4- \sqrt{4}}{2}=\frac{4-2}{2}= \frac{2}{2}=1$