Question

ME AJUDEM, é Pra amanhã
8-A equação (0,5)X=1/16
em R
vale:
a) x = 2
b) x = 3
c) x =4
d) x =5
e) x =6

9-O conjunto solução, em R, da equação exponencial 10%, 10x+ 2 = 1000 é:
A)1
B)2
C)3
D)1/3
E)1/2

10. Para que o resultado da função f(x)= 4x+2x+4 seja igual a 256, qual é o valor de x?
a) o
b) 2
c) 6
d) 8
e) 10

Answer 1

$\large\boxed{\begin{array}{l}\sf 5)\,Marque\,a\,alternativa\,que\,cont\acute em\,o\,conjunto\\\sf de\,soluc_{\!\!,}\tilde oes\,da\,equac_{\!\!,}\tilde ao\,exponencial:\\\sf 2^{2-x}=\dfrac{1}{8}\\\\\sf a)1~~~~~~~b)2~~~~~~~c)3~~~~~~~d)4~~~~~~~\bullet e)5\\\underline{\sf soluc_{\!\!,}\tilde ao\!:}\\\rm 2^{2-x}=\dfrac{1}{8}\\\\\rm 2^{2-x}=2^{-3}\\\rm 2-x=-3\\\rm x=2+3\\\rm x=5\end{array}}$

$\large\boxed{\begin{array}{l}\sf6)\,Resolva\,a\,equac_{\!\!,}\tilde ao\,exponencial:3^x=27\\\sf a)-1~~~~~~~b)0~~~~~~~c)1~~~~~~~d)2~~~~~~~\bullet e)3\\\underline{\sf soluc_{\!\!,}\tilde ao\!:}\\\rm 3^x=27\\\rm 3^x=3^3\\\rm x=3\end{array}}$

$\large\boxed{\begin{array}{l}\sf 7)\,O\,resultado\,da\,equac_{\!\!,}\tilde ao\,exponencial\\\sf 2^{x+3}+2^{x-1}=17\,tem\,soluc_{\!\!,}\tilde ao\,para:\\\sf a)x=0~~~~~~~b)x=2~~~~~~~\bullet c)x=1~~~~~~~d)x=3~~~~~~~e)x=-2\\\underline{\sf soluc_{\!\!,}\tilde ao\!:}\\\rm 2^{x+3}+2^{x-1}=17\\\rm 2^{x}\cdot 2^3+\dfrac{2^x}{2}=17\bullet(2)\\\rm 2\cdot2^x\cdot2^3+2^x=34\\\rm 2^x(2^4+1)=34\\\rm 2^x\cdot17=34\\\rm 2^x=\dfrac{34}{17}\\\\\rm 2^x=2\\\rm x=1\end{array}}$

$\large\boxed{\begin{array}{l}\sf 8) A\,equac_{\!\!,}\tilde ao\,(0,5)^x=\dfrac{1}{16}\,em\,\mathbb{R}\,vale:\\\sf a)x=2~~~~~~~b)x=3~~~~~~~\bullet c)x=4~~~~~~~d)x=5~~~~~~~e)x=6\\\underline{\sf soluc_{\!\!,}\tilde ao\!:}\\\rm (0,5)^x=\dfrac{1}{16}\\\\\rm\bigg(\dfrac{1}{2}\bigg)^x=\bigg(\dfrac{1}{2}\bigg)^4\\\\\rm x=4\end{array}}$

$\large\boxed{\begin{array}{l}\sf 9) O\,conjunto\,soluc_{\!\!,}\tilde ao,em\,\mathbb{R},\,da\,equac_{\!\!,}\tilde ao\,exponencial\\\sf 10^x\cdot10^{x+2}=1000\,\acute e:\\\sf a)1~~~~~~~b)2~~~~~~~c)3~~~~~~~d)\dfrac{1}{3}~~~~~~~\bullet e)\dfrac{1}{2}\\\underline{\sf soluc_{\!\!,}\tilde ao\!:}\\\rm 10^x\cdot10^{x+2}=1000\\\rm 10{x+x+2}=1000\\\rm 10^{2x+2}=10^3\\\rm 2x+2=3\\\rm 2x=3-2\\\rm 2x=1\\\rm x=\dfrac{1}{2}\end{array}}$

$\large\boxed{\begin{array}{l}\sf 10)\,Para\,que\,o\,resultado\,da\,func_{\!\!,}\tilde ao\,f(x)=4^{x+2x+4}\,seja\,256\\\sf qual\,\acute e\,o\,valor\,de\,x?\\\sf \bullet a)0~~~~~~~b)2~~~~~~~c)6~~~~~~~d)8~~~~~~~e)10\\\underline{\sf soluc_{\!\!,}\tilde ao\!:}\\\rm 4^{x+2x+4}=256\\\rm 4^{3x+4}=4^4\\\rm 3x+4=4\\\rm 3x=4-4\\\rm 3x=0\\\rm x=\dfrac{0}{3}\\\\\rm x=0\end{array}}$

$\large\boxed{\begin{array}{l}\rm espero\,que\,tenha\,ajudado\,\heartsuit\end{array}}$