Question

Resolva as seguintes equações exponencias na variável x

a) 2^x = 64
b) 3^x-2= 9
c) 5^x2 - ^x2 = 125
d) 10^1-^x =1/10
e) 2^4x-^x2= 8
f) (10^x)^1-x= 0,000001
g) 3^2 -x = 1/27
h) 3^x-5= 27^1-x

Ajuda aq pelo amor d Deus

Answer 1

a)
$2^x=64\\\\2^x=2^6\\\\x=6$

b)
$3^{x-2}=9\\\\3^{x-2}=3^2\\\\x-2=2\\\\x=4$

c)
$5^{x^2-2x}=125\\\\5^{x^2-2x}=5^3\\\\x^2-2x=3\\\\x^2-2x-3=0\\\\x_1=3\\\\x_2=-1$

d)
$10^{1-x}=\dfrac{1}{10}\\\\10^{1-x}=10^{-1}\\\\1-x=-1\\\\x=2$

e)
$2^{4x-x^2}=8\\\\2^{4x-x^2}=2^3\\\\4x-x^2=3\\\\x^2-4x+3=0\\\\x_1=3\\\\x_2=1$

f)
$(10^x)^{1-x}=0,000001\\\\(10^x)^{1-x}=10^{-6}\\\\10^{x-x^2}=10^{-6}\\\\x-x^2=-6\\\\x^2-x-6=0\\\\x_1=3\\\\x_2=-2$

g)
$3^{2-x}=\dfrac{1}{27}\\\\3^{2-x}=27^{-1}\\\\3^{2-x}=3^{-3}\\\\2-x=-3\\\\x=5$

h)
$3^{x-5}=27^{1-x}\\\\3^{x-5}=3^{3-3x}\\\\x-5=3-3x\\\\4x=8\\\\x=2$