Question

...resolva as seguintes equações exponenciais: 
A)10( elevado na 1-4x) = 0,001
B) 6.7(elevado na x+2) = 294
C) 2. (1/2) (elevado na 2x-3) =4
D) 4 (elevado na x)= ³ raiz de 32

Answer 1

Para resolver equações exponenciais, é importante ter em mente que devemos igualar as bases, para poder igualar os expoentes.

$a)10^{1-4x}=10^{-3}\\1-4x=-3\\-4x=-4\\x=1$

$b)6.7^{x+2}=294\\7^{x+2}= \frac{294}{6} \\7^{x+2}=49\\7^{x+2}=7^2\\x+2=2\\x=0$

$c)2. (\frac{1}{2}) ^{2x-3}=4$

$( \frac{1}{2})^{2x-3}=2^1\\2x-3=1\\2x=2\\x=1$

$d)4^x= \sqrt[3]{32}\\2^{2x}= \sqrt[3]{2^5} \\2^{2x}=2^{5/3}\\2x= \frac{5}{3} \\x= \frac{5}{6}$

Answer 2

a)
$10^{1-4x}= 0,001\\ 10^{1-4x}= 10^{-3}\\ 1-4x= -3\\ -4x=-3-1\\ 4x=4\\ x= \frac{4}{4} \\ \\ x=1$

b)
$6.7^{x+2}=294 \\ \\ 7^{x+2}= \frac{294}{6} \\ \\ 7^{x+2}= 49 \\ 7^{x+2}= 7^2 \\ x+2=2 \\ x=2-2 \\ x=0$

c)
$2.(\frac{1}{4})^{2x-3}= 4 \\ \\ (\frac{1}{4})^{2x-3}= \frac{4}{2} \\ (2^{-2})^{2x-3}= 2^1 \\ 2^{-4x+6}= 2^1\\ -4x+6=1\\ -4x= 1-6 \\ x= \frac{-5}{-4}\\ x= \frac{5}{4}$

d)
$4^x= \sqrt[3]{32} \\ (2^2)^x= \sqrt[3]{2^5} \\ 2^{2x}= 3^\frac{5}{3}\\ 2x= \frac{5}{3} \\ x= \frac{5}{3} : 2 \\ \\ x= \frac{5}{3} . \frac{1}{2} \\ \\ x= \frac{5}{6}$