Question

Resolva as equações:

a) 2^x = 256
b) 4^x = 32
c) 2^x = 1/8
d) 2^x = ³√4
e) 9^x+3 = 27^x
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Answer 1

$\large\boxed{\begin{array}{l}\tt a)~\sf 2^x=256\\\sf 2^x=2^8\\\sf x=8\\\tt b)~\sf 4^x=32\\\sf (2^2)^x=2^5\\\sf 2^{2x}=2^5\\\sf 2x=5\\\sf x=\dfrac{5}{2}\end{array}}$

$\large\boxed{\begin{array}{l}\tt c)~\sf 2^x=\dfrac{1}{8}\\\\\sf 2^x=2^{-3}\\\sf x=-3\\\tt d)~\sf 2^x=\sqrt[\sf3]{\sf4}\\\sf 2^x=2^{\frac{2}{3}}\\\sf x=\dfrac{2}{3}\\\\\tt e)~\sf 9^{x+3}=27^x\\\sf 3^{2x+6}=3^{3x}\\\sf 2x+6=3x\\\sf 3x-2x=6\\\sf x=6\end{array}}$