Question

Resolva em R as equações (apresente os cálculos)
a) (V0,1)^x = ^3V10
b) (3/5)^-x+2 = 3^V5/3
c) (5/3)^-x+1 = ^3V9/25

Answer 1

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d)
$\sqrt{0,1^x}= 10^{ \frac{1}{3} } \\ \\ ( \frac{1}{10} )^{ \frac{x}{2} }=10^{ \frac{1}{3} } \\ \\\not 10^{- \frac{x}{2}}=\not10^{ \frac{1}{3} } \\ \\ - \frac{x}{2} = \frac{1}{3} \\ \\ -3x= 2 \\ \\ 3x=-2 \\ \\ x=- \frac{2}{3}$

e)

$( \frac{3}{5} )^{-x+2}= (\frac{5}{3} )^{ \frac{1}{3} } \\ \\ (\frac{3}{5})^{-x+2 }=( \frac{3}{5} )^{- \frac{1}{3} } \\ \\ -x+2=- \frac{1}{3} \\ \\ -3x+6=-1 \\ \\ -3x=-1-6 \\ \\ -3x=-7 \\ \\ 3x=7 \\ \\ x= \frac{7}{3}$ 

f)

$( \frac{5}{3} )^{-x+1}=( \frac{9}{5} )^{ \frac{1}{3} } \\ \\ ( \frac{5}{3} ){-x+1}=[( \frac{3}{5} )^2]^{ \frac{1}{3} } \\ \\ ( \frac{5}{3})^{-x+1}=( \frac{5}{3} )^{- \frac{2}{3} } \\ \\ -x+1=- \frac{2}{3} \\ \\ -3x+3=-2 \\ \\ -3x=-2-3 \\ \\ -3x=-5 \\ \\ 3x=5 \\ \\ x= \frac{5}{3}$