Question

Resolva a inequação exponencial
$(0,5)^{x-1} + (0,5) ^{x-2} \leq 48$

Answer 1

Rebeca,

Vamos resolver passo-a-passo

         $(0,5) ^{x-1} + (0,5)^{x-2} \leq 48 \\ \\ ( \frac{1}{2} )^x.( \frac{1}{2} ) ^{-1} +( \frac{1}{2}) ^{x} .( \frac{1}{2} ) ^{-2} \leq 3.2^4 \\ \\ ( \frac{1}{2}) ^{x}{ [( \frac{1}{2} ) ^{-1} +( \frac{1}{2}) ^{-2} ] \leq 3.2^4$

         $(\frac{1}{2} )^x(2+4) \leq 3.2^4 \\ \\ 2^{-x} \leq \frac{3.2.2^3}{6} \\ \\ 2^{-x} \leq 2^3 \\ \\ -x \leq 3 \\ \\ x \geq -3$