Question

Resolva as equaçoes

a) 7 elevado a x= 1/2401

b) 3 elevado a x+2 - 3 elevado a x+1+ 3elevado a x-2 + 3 elevado a x-3= 1494

Answer 1

a)

$7^x= \frac{1}{2401}$

$7^x= \frac{1}{7^4}$

$7^x=7^-^4 \\ x=-4$

S={-4}

b)
$3^{x+2} - 3^{x+1} + 3^{x-2} + 3^{x-3} =1494 \\ 3^x.3^2-3^x.3^1+3^x.3^-^2+3^x.3^-^3=1494 \\ 3^x(3^2-3+3^-^2+3^-^3)=1494$

$3^x(9-3+ \frac{1}{9} + \frac{1}{27} )=1494$

$3^x(6+ \frac{1}{9} + \frac{1}{27} )=1494$

$3^x( \frac{162+3+1}{27} )=1494$

$3^x( \frac{166}{27} )=1494$

$3^x=1494: \frac{166}{27}$

$3^x=1494. \frac{27}{166}$

$3^x=9.27 \\ 3^x=243 \\ 3^x=3^5 \\ x=5$

S={ 5 }