Question

qual a equação exponecial de :

a ) , b) , c ), d) e E) ?

Answer 1

$a)\\3^x=3^4\\\\x=4$

$b)\\5^{5x^2-2x}=5^3\\\\5x^2-2x=3\\\\5x^2-2x-3=0\\\\\Delta=(-2)^2-4.5.(-3)\\\Delta = 4 + 60\\\Delta = 64\\\\x_1=\frac{2+\sqrt{64}}{2.5}=\frac{2+8}{10}=1\\x_2=\frac{2-\sqrt{64}}{2.5}=\frac{2-8}{10}=-\frac{3}{5}$

$c)\\10^{x.(1-x)}=10^{-6}\\\\x.(1-x)=-6\\\\-x^2+x+6=0\\\\\Delta = 1^2-4.(-1).6\\\Delta = 1+24\\\Delta = 25\\\\x_1=\frac{-1+\sqrt{25}}{2.(-1)}=\frac{-1+5}{-2}=-2\\x_2=\frac{-1-\sqrt{25}}{2.(-1)}=\frac{-1-5}{-2}=3$

$d)\\2^{\frac{x}{5}}=32^{-1}\\\\2^{\frac{x}{5}}=2^{5^{-1}}\\\\2^{\frac{x}{5}}=2^{-5}\\\\\frac{x}{5}=-5\\\\x=-25$

$e)\\2^{-1^{x^2-4}}=32^{-1}\\\\2^{-x^2+4}=2^{-5}\\\\-x^2+4=-5\\\\x^2=9\\\\x=\pm \sqrt{9}\\\\x=\pm 3$