Question

use a definição para calcular log^2 1/4

Answer 1

Logaritmo

$\boxed{ \mathsf{Log_{a}b=x \to a^{x} = b}}$

a)

$2^{x} = \frac{1}{4} \\ \\ 2^{x} = 4^{-1} \\ 2^{x} = 2^{-2} \\ x = -2$

b)

$3^{x} = 3^{\frac{1}{2}} \\ \\ x = \frac{1}{2}$

c)

$8^{x} = 2^{4} \\ 2^{3x} = 2^{4} \\ \\ 3x = 4 \\ x = \frac{4}{3}$

d)

$4^{x} = 2^{7} \\ 2^{2x} = 2^{7} \\ 2x = 7 \\ x = \frac{7}{2}$

e)

$6^{2x} = 6^{\frac{1}{2}} \\ 2x = \frac{1}{2} \\ x = \frac{1}{4}$

f)

$10^{x} = \frac{1}{100} \\ \\ 10^{x} = 10^{-2} \\ x = -2$

g)

$(3^{2})^{x} = 27^{-1} \\ 3^{2x} = 3^{-3} \\\\ 2x = -3 \\ x = \frac{-3}{2}$

h)

$(\frac{2}{10})^{x} = \sqrt[3]{5^{2}} \\ \\ (\frac{1}{5})^{x} = 5^{\frac{2}{3}} \\ \\ 5^{-x} = 5^{\frac{2}{3}} \\ x = \frac{-2}{3}$

i)

$(\frac{125}{100})^{x} = (\frac{64}{100})\\ \\ (\frac{5}{4})^{x} = \frac{16}{25} \\ \\ (\frac{5}{4})^{x} = (\frac{5}{4})^{-2} \\ x = -2$

j)

$(\frac{5}{3})^{x} = (\frac{6}{10}) \\ \\ (\frac{5}{3})^{x} = (\frac{5}{3})^{-1} \\ x = -1$