Question

a)x^2:(3^2)^2=x^2
B)196:x^2=7^4:7^2
C)111(x)=73(10)
D)324:5^x=(2•3^2)^2

Answer 1

 

$\displaystyle\bf\\a)\\x^2:\Big(3^2\Big)^2=2^2\\\\x^2:3^{2\times2}=2^2\\x^2:3^4=2^2\\x^2=2^2\times3^4\\x=\sqrt{2^2\times3^4}\\x= 2\times3^2\\x=2\times9\\\boxed{\bf x=18}\\\\b)\\196:x^2=7^4:7^2\\196:x^2=7^{4-2}\\196:x^2=7^2\\\\x^2=\frac{196}{7^2}\\\\x^2=\frac{4\times49}{7^2}\\\\x^2=\frac{4\times7^2}{7^2}\\\\x^2=4\\\\x=\sqrt{4}\\\\\boxed{\bf x=2}$

.

$\displaystyle\bf\\c)\\111_{(x)}=73_{(10)}\\\\Numerotam~cifrele.\\\\\overset{2}{1}\overset{1}{1}\overset{0}{1}_{(x)}=73_{(10)}\\\\Convertim~in~baza~(10)~numarul~scris~in~baza~(x).\\\\1\times x^2+1\times x^1+1\times x^0=73\\\\Scriem~ecuatia.\\\\x^2+x+1=73\\\\x^2+x+1-73=0\\\\x^2+x-72=0\\\\x_{12}=\frac{-1\pm\sqrt{1+4\times72}}{2}=\frac{-1\pm\sqrt{1+288}}{2}=\frac{-1\pm\sqrt{289}}{2}=\frac{-1\pm17}{2}\\\\x_1=\frac{-1+17}{2}=\frac{16}{2}=8x_2<0~solutie eliminata\\\\\implies~\boxed{\bf x=8}$

.

$\displaystyle\bf\\324:5^x=\Big(2\times3^2\Big)^2\\\\324:5^x=2^2\times3^4\\\\324:5^x=4\times81\\\\324:5^x=324\\\\5^x=324:324\\\\5^x=1\\\\\implies~\boxed{\bf x=0}$