Question

a equação exponencial (0,16)^-1=(2/5)^x/3 tem como soluçao?

>a)-1
b)2
c)-3
d)-5
e)-6

com resoluçao pfv

Answer 1

$(0,16)^{-1} = ( \frac{2}{5} )^{ \frac{x}{3} } \\ \\ ( \frac{16}{100} )^{-1} = ( \frac{2}{5} )^{ \frac{x}{3} } \\ \\ ( \frac{4}{25} )^{-1} = ( \frac{2}{5} )^{ \frac{x}{3} } \\ \\ ( \frac{ 2^{2} }{ 5^{2} } )^{-1} = ( \frac{2}{5} )^{ \frac{x}{3} } \\ \\ ( (\frac{ 2 }{ 5 })^{2} )^{-1} = ( \frac{2}{5} )^{ \frac{x}{3} } \\ \\ ( \frac{ 2 }{ 5 } )^{-2} = ( \frac{2}{5} )^{ \frac{x}{3} } \\ \\ -2 = \frac{x}{3} \\ \\ x = -2.3 \\ \\ x = -6$