Question

só a letras g), h), o) e p), alguém pode me ajudar resolver com os cálculos, por favor

Answer 1

g)

$5^x = \sqrt[3]{625} \\\\ 5^x = \sqrt[3]{5^4} \\\\ 5^x = 5^{ \frac{4}{3} } \\\\ \boxed{ x = { 4 \over 3}}$

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h)

$2^x = \sqrt{32} \\\\ 2^x = \sqrt{2^5} \\\\ 2^x = 2^{\frac{5}{2}} \\\\ \boxed{ x = { 5 \over 2} }$

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o)

$5^{x-2} = 25^{2x} \\\\ 5^{x-2} = (5^2)^{2x} \\\\ 5^{x-2} = 5^{4x} \\\\ x - 2 = 4x \\\\ \boxed{ x = -{2 \over 3} }$

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p)

$(3^x)^{x-1} = 9 \\\\ 3^{x^2 - x} = 3^2 \\\\ x^2 - x = 2 \\\\ x^2 - x - 2 = 0 \\\\ x^2 + x - 2x - 2 = 0 \\\\ x(x +1 ) -2(x +1) = 0 \\\\ (x-2)(x+1) = 0 \\\\ \boxed{ x_1 = 2 } \\\\ \boxed{ x_2 = -1 }$