Question

3) Resolva, em IR, as exponenciais abaixo:
a) 2^3x = 64
b) 3^x+ 1 = 27
c) 8.2^x = 128
d) 4.2^x = 16
e) √8^x = 1024​

Answer 1

Olá!

$a)~2^{3x}=64\\ \\ ~~~~~2^{3x}=~2^{6}\\ \\ ~~~~~3x=6\\ \\ ~~~~~x=\dfrac{6}{3}\\ \\ ~~~~~ \\~~~~~ \boxed{x=2}$

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$b)~3^{x+1}=27\\ \\ ~~~~3^{x+1}=3^{3}\\ \\~~~~ x+1=3\\ \\~~~~ x=3+1\\ \\ ~~~~\boxed{x=4}$

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$c)~8\cdot 2^{x}=128\\ \\ \\ ~~~~~2^{x}=\dfrac{128}{8} \\ \\ ~~~~~2^{x}=16\\ \\ ~~~~~2^{x}=2^{4}\\ \\~~~~~ \boxed{x=4}$

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$d)~4\cdot 2^{x}=16\\ \\ \\ ~~~~~2^{x}=\dfrac{16}{4} \\ \\ ~~~~~2^{x}=4\\ \\ ~~~~~2^{x}=2^{2}\\ \\~~~~~ \boxed{x=2}$

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$e)~\sqrt{8^{x}}=1024\\ \\ (8^{x})^{\frac{1}{2} } =2^{10}\\ \\ 8^{\frac{x}{2} =2^{10}}\\ \\ (2^{3})^{\frac{x}{2} }=2^{10}\\ \\\\ \dfrac{3x}{2} =10\\ \\\\ 3x=10\cdot2\\ \\ 3x=20\\ \\ \boxed{x=\dfrac{20}{3} }$

:)