Question

1)resolver as equações logarítmicas:

a) log8 (8x + 5) =log8 (x + 26)

b) log4 (7x +2)= 2

C) log2 (x² -7x + 18)= 3​

Answer 1

a) x = 3

$log_{8} \: (8x + 5) = log_{8} \: (x + 26) \\ 8x + 5 = x + 26 \\ 8x - x = 26 - 5 \\ 7x = 21 \\ x = \frac{21}{7} = 3$

b) x = 2

$log_{4} \: (7x + 2) = 2 \\ {4}^{2} = 7x + 2 \\ 16 - 2 = 7x \\ 14 = 7x \\ x = \frac{14}{7} = 2$

c) x' = 5; x" = 2

$log_{2}( {x}^{2} - 7x + 18) = 3 \\ {x}^{2} - 7x + 18 = {2}^{3} \\ {x}^{2} - 7x + 18 = 8 \\ {x}^{2} - 7x + 18 - 8 = 0 \\ {x}^{2} - 7x + 10 = 0$

$x = \frac{-b±\sqrt{b^2-4ac}}{2a}$

$x = \frac{-( - 7)±\sqrt{( - 7)^2-4 \times 1 \times 10}}{2 \times 1} \\ x = \frac{7± \sqrt{49 - 40} }{2} \\ x = \frac{7± \sqrt{9} }{2} = \frac{7±3}{2} \\ x_1 = \frac{7 + 3}{2} = \frac{10}{2} = 5 \\ x_2 = \frac{7 - 3}{2} = \frac{4}{2} = 2$