Question

Considerando log 2 = 0,30 e log 3 = 0,48, o numero real X que satisfaz a equação $2^{x+3} = 6$ é

Answer 1

$2^{x+3}=6\\2^{x+3}=2.3\\\\\frac{2^{x+3}}{2}=3\\\\2^{x+3-1}=3\\2^{x+2}=3\\\\\log(2^{x+2})=\log(3)\\(x+2).\log(2)=\log(3)\\\\\log(2)\approx0,3\\\log(3)\approx0,48\\\\(x+2).0,3=0,48\\0,3x+0,6=0,48\\0,3x=0,48-0,6\\0,3x=-0,12\\\\x=\frac{-0,12}{0,3}\\\\\boxed{x=-0,4}$

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