Question

Qual o valor da expressão y =

Answer 1

$log_{9} \sqrt{3}$

$\sqrt{3} = 9^{x} \\ \\ 3^{\frac{1}{2}} = 9^{x} \\ \\ 3^{\frac{1}{2}} = (3^{2})^{x} \\ \\ 3^{\frac{1}{2} } = 3^{2x} \\ \\ \frac{1}{2} = 2x \\ \\ \frac{\frac{1}{2}}{2} = x \\ \\ \frac{1}{2} . \frac{1}{2} = x \\ \\ \frac{1}{4} = x$

$log_{10} 0,01$

$0,01 = 10^{y} \\ \frac{1}{100} = 10^{y} \\ 100^{-1} = 10^{y} \\ (10^{2})^{-1} = 10^{y} \\ 10^{-2} = 10^{y} \\ -2 = y$

$log_{2} \frac{1}{64}$

$\frac{1}{64} = 2^{z} \\ 64^{-1} = 2^{z} \\ (2^{6})^{-1} = 2^{z} \\ 2^{-6} = 2^{z} \\ -6 = z$

$log_{4} \sqrt{8}$

$\sqrt{8} = 4^{a} \\ \\ 8^{\frac{1}{2}} = 4^{a} \\ \\ (2^{3})^{\frac{1}{2}} = (2^{2})^{a} \\ \\ 2^{\frac{3}{2}} = 2^{2a} \\ \\ \frac{3}{2} = 2a \\ \\ \frac{\frac{3}{2}}{2} = a \\ \\ \frac{3}{2} . \frac{1}{2} = a \\ \\ \frac{3}{4} = a$

A expressão vai ficar assim:

$y = \frac{\frac{1}{4} + (-2)}{(-6) + \frac{3}{4}} \\ \\ y = \frac{\frac{1}{4} - 2}{-6 + \frac{3}{4}} \\ \\ y = \frac{\frac{-7}{4}}{\frac{-21}{4}} \\ \\ y = \frac{-7}{4} . \frac{4}{-21} \\ \\ y = \frac{-28}{-84} \\ \\ y = \frac{1}{3}$

Espero ter ajudado!
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