Question

Equação exponencial. Ajuda???

Answer 1

b)

$(0,04)^x =125\\\\ (\frac{4}{100}) ^x = 125\\\\ (\frac{1}{25})^x = 125\\\\ 5^-^2^x = 5^3\\\\ \boxed{x=-\frac{3}{2}}$

c)

$2^x^+^1 = 0,125\\\\ 2^x^+^1 = \frac{125}{1000}\\\\ 2^x^+^1 = \frac{1}{8}\\\\ 2^x^+^1 = 2^-^3\\\\ x+1 = -3\\\\ \boxed{x=-4}$

d)

$(\frac{1}{16})^x^-^1 = 2^x^-^2\\\\\ (2^-^4)^x^-^1 = 2^x^-^2\\\\ 2^-^4^x^+^4 = 2^x^-^2\\\\\ -4x+4 = x-2\\\\ -4x-x = -2-4\\\\ -5x = -6\\\\ \boxed{x=\frac{6}{5}}$

e)

$81^x = 27^x^-^5\\\\ 3^4^x = (3^3)^x^-^5\\\\ 3^4^x = 3^3^x^-^1^5\\\\ 4x=3x-15\\\\ 4x-3x = -15\\\\ \boxed{x=-15}$