Question

resolva as equações exponenciais:

Answer 1

42)
a)
$2. 3^{x-2}=162 \\ 3^{x-2}= \frac{162}{2} \\ 3^{x-2}=81 \\ 3^{x}. 3^{-2}=81 \\ 3^{x}.(\frac{1}{3})^{2}=81 \\ \\ 3^{x}. \frac{1}{9}=81 \\ 3^{x}= \frac{9}{1} .81 \\ 3^{x}=729 \\ 3^{x} = 3^{6} \\ \\ x=6$

b)
$3. 5^{x-1}=75 \\ 5^{x-1}= \frac{75}{3} \\ 5^{x-1}=25 \\ 5^{x}. 5^{-1}=25 \\ 5^{x}. \frac{1}{5}=25 \\ 5^{x}=5.25 \\ 5^{x}=125 \\ 5^{x}=5^{3} \\ x=3$

c)
$5. 2^{x^{2}-4}=160\\2^{x^{2}-4}= \frac{160}{5}\\ 2^{ x^{2}-4}=32\\ 2^{ x^{2}-4}=2^5\\x^{2}-4=5\\x^2=9\\x= \sqrt{9}\\x'=3\\e\\x''=-3$

d)
$10.2^{x+3}=10 \\ 2^{x+3}= \frac{10}{10}\\2^{x+3}=1\\2^{x+3}=2^{0}\\x+3=0\\x=-3$