Question

Qual o resultado das seguintes equações: 2^-x = 64^x+5 /// ³√4^x =2 /// 1/5^x/2 = 0.04

Answer 1

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$2^{-x}=64^{x+5} \\ 2^{-x}=(2^6)^{x+5} \\\not 2^{-x}=\not2^{6x+30} \\ \\ -x=6x+30 \\ -x-6x=30 \\ -7x=30~~\times(-1) \\ 7x=-30 \\ x=- \frac{30}{7}$ 

b)
$\sqrt[3]{4^x} =2 \\ 4^{ \frac{x}{3}} =2 \\ \\ (2^2)^{ \frac{x}{3} }=2 \\ \\ \not2^{ \frac{2x}{3} }=\not2^1 \\ \\ \frac{2x}{3} =1 \\ \\ 2x=3 \\ x= \frac{3}{2}$ 

c)
$( \frac{1}{5} )^{ \frac{x}{2}} = \frac{4}{100} \\ \\ ( \frac{1}{5} )^{ \frac{x}{2} }= \frac{1}{25} \\ \\ ( \frac{1}{5} )^{ \frac{x}{2} }=( \frac{1}{5} )^2 \\ \\ \frac{x}{2} =2 \\ \\ x=4$