Question

Resolva as seguintes equações exponenciais em R

Answer 1

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a)

$\sf{\left(\dfrac{1}{5}\right)^x=125}\\\sf{5^{-x}=5^3}\\\sf{-x=3\cdot(-1)}\\\sf{x=-3}$

b)

$\sf{\left(\dfrac{1}{3}\right)^x=729}\\\sf{3^{-x}=3^6}\\\sf{-x=6\cdot(-1)}\\\sf{x=-6}$

c)

$\sf{\left(\sqrt[4]{3}\right)^x=81}\\\sf{3^{\frac{x}{4}}=3^4}\\\sf{\dfrac{x}{4}=4}\\\sf{x=4\cdot4}\\\sf{x=16}$

d)

$\sf{(\sqrt[6]{2})^x=0,5}\\\sf{2^{\frac{x}{6}}=2^{-1}}\\\sf{\dfrac{x}{6}=-1}\\\sf{x=6\cdot(-1)}\\\sf{x=-6}$