Question

6. Resolva a seguinte equação: 2^x+2^x+1+2^x+2=112

7. Determine os valores de x que satisfazem a equação:

2^2x+1 1
_____=_
2^4x-3 2

8. Determine a soma dos valores de x que satisfazem a equação:
25^x-24×5^x-25=0

9. Resolva as equações:
a) 3^2x-28×3^x+27=0
b) 2^2x=12×2^x-32​

Answer 1

$\Large\boxed{\begin{array}{l}\rm 6)\\\sf 2^x+2^{x+1}+2^{x+2}=112\\\sf 2^x+2^x\cdot 2+2^x\cdot 4=112\\\sf 2^x(1+2+4)=112\\\sf 2^x\cdot7=112\\\sf 2^x=\dfrac{112}{7}\\\sf 2^x=16\\\sf 2^x=2^4\\\sf x=4\end{array}}$

$\Large\boxed{\begin{array}{l}\rm 7)\\\\\sf\dfrac{2^{2x+1}}{2^{4x-3}}=\dfrac{1}{2}\\\\\sf 2^{2x+1-4x+3}=2^{-1}\\\sf2^{-2x+4}=2^{-1}\\\sf -2x+4=-1\\\sf 2x=4+1\\\sf 2x=5\\\sf x=\dfrac{5}{2}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf As~quest\tilde oes~~8~e~9~s\tilde ao~ileg\acute iveis.\end{array}}$