Question

me ajudem nessa esqução 5*2^x = 4^x

Answer 1

Olá!

$\\ 5 \cdot 2^x = 4^x \\\\ 5 \cdot 2^x = (2^2)^x \\\\ (2^x)^2 - 5 \cdot 2^x = 0 \\\\ 2^x(2^x - 5) = 0$

 Factor I:

$\\ 2^x = 0 \\\\ \boxed{S_I = \varnothing}$


 Factor II:

$\\ 2^x - 5 = 0 \\\\ 2^x = 5 \\\\ \log_2 5 = x \\\\\boxed{S_{II} = \left \{ \log_2 5 \right \}}$