a)
[tex] 3^{x+1} = 81 \\ 3^{x+1} = 3^{4} \\ x+1=4 \\ =>x=4-1 \\ x=3[/tex]
b)
[tex] 2^{x} = \frac{1}{16} \\ 2^{x} = \frac{1}{ 2^{4}} \\2^{x} =2^{-4} \\ x=-4 [/tex]
c)
[tex] lg x=-2 \\ 10^{-2} =x \\ x= \frac{1}{10^{2}}= \frac{1}{100} \\ x=0,01 [/tex]
d)
[tex]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[/tex]
