Question

AJUDAAA
Resolvendo a equação 2^2x + 1 = 8^x-1, em R, obtemos a seguinte solução:

Answer 1

$\Large\boxed{\begin{array}{l}\rm O\,conjunto\,soluc_{\!\!,}\tilde ao,da\,equac_{\!\!,}\tilde ao\,exponencial\\\rm 10^{x+2}=1000~\acute e:\\\underline{\boldsymbol{soluc_{\!\!,}\tilde ao\!:}}\\\sf 10^{x+2}=1000\\\sf 10^{x+2}=10^3\\\sf x+2=3\\\sf x=3-2\\\sf x=1\\\blue{\huge\boxed{\boxed{\boxed{\boxed{\sf S=\{1\}}}}}}\green{\checkmark}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm Resolvendo\,a\,equac_{\!\!,}\tilde ao~2^{2x+1}=8^{x-1},em\,\mathbb{R},\\\rm obtemos\,a\,seguinte\,soluc_{\!\!,}\tilde ao\!:\\\underline{\boldsymbol{soluc_{\!\!,}\tilde ao\!:}}\\\sf 2^{2x+1}=8^{x-1}\\\sf 2^{2x+1}=(2^3)^{x-1}\\\sf 2^{2x+1}=2^{3x-3}\\\sf 2x+1=3x-3\\\sf 2x-3x=-3-1\\\sf -x=-4\cdot(-1)\\\sf x=4\\\huge\boxed{\boxed{\boxed{\boxed{\blue{\sf S=\{4\}}\green{\checkmark}}}}}\end{array}}$