Question

Dadas as equações exponenciais:

a) 4^(x)= 512

b)2^(y) + 2^(y + 1) = 24

c)3 . 2^ (z + 1) - 4 . 2^( z – 2) - 6 . 2^ (z) = - 4

Answer 1

$a) \\ \\ \: 4^x = 512 \\ {({2}^{2})}^{x} = 2^9 \\ {2}^{2x} = 2^9 \\ 2x = 9 \\ \\ \boxed{x = \frac{9}{2}} \\ \\ -------------------- \\ b) \\ \\ \: 2^y + {2}^{y+1} = 24 \\ 2^y \times (2+1) = 24 \\ 3 \times 2^y = 24 \\ 2^y = 8 \\ 2^y= 2^3 \\ \\ \boxed{y = 3} \\ \\ --------------------- \\ c) \\ \\ \: 3 \times {2}^{z+1} - 4 \times {2}^{z-2} - 6 \times 2^z = -4 \\ {2}^{z-2} \times (3 \times 2^3 -4 -6 \times 2^2) = -4 \\ {2}^{z-2} \times ( 24-4-24) = -4 \\ -4 \times {2}^{z-2} = -4 \\ {2}^{z-2} = 1 \\ {2}^{z-2} = 2^0 \\ z - 2 = 0 \\ \\ \boxed{z = 2}$