Question

resolva as equações exponenciais ​

Answer 1

Explicação passo-a-passo:

a)

$2^{x+4}=64\\\\ 2^{x+4}=2^{6}\\\\\text Igualando\ os\ expoentes:\\\\x+4=6\\\\x=6-4\\\\x=2\\\\\boxed{\boxed{S=\{2\}}}$

b)

$9^{2x+3}=3\\\\ (3^{2} )^{2x+3}=3^{1}\\\\ 3^{2.(2x+3)}=3^{1} \\\\\text Igualando\ os\ expoentes:\\\\2.(2x+3)=1\\\\4x+6=1\\\\4x=1-6\\\\4x=-5\\\\x=\dfrac{-5}{4} \\\\\boxed{\boxed{S=\bigg\{\dfrac{-5}{4}\bigg\}}}$

c)

$16^{x+4}=64\\\\(2^{4}) ^{x+4} =2^{6} \\\\2^{4.(x+4)} =2^{6} \\\\\text Igualando\ os\ expoentes:\\\\4.(x+4)=6\\\\4x+16=6\\\\4x=6-16\\\\4x=-10\\\\x=\dfrac{-10}{4}\\\\x= \dfrac{-5}{2}\\\\\boxed{\boxed{S=\bigg\{ \dfrac{-5}{2}\bigg\}}}$

d)

$2^{x-5}=1\\\\ 2^{x-5}=2^{0}\\\\\text Igualando\ os\ expoentes:\\\\x-5=0\\\\x=5\\\\\boxed{\boxed{S=\{5\}}}$

e)

$9^{4x+1} =27^{x+4}\\\\(3^{2}) ^{4x+1}=(3^{3}) ^{x+4}\\\\3 ^{2.(4x+1)}=3 ^{3.(x+4)}\\\\\text Igualando\ os\ expoentes:\\\\2.(4x+1)=3.(x+4)\\\\8x+2=3x+12\\\\8x-3x=12-2\\\\5x=10\\\\x=\dfrac{10}{5}\\\\x=2\\\\\boxed{\boxed{S=\{2\}}}$