Question

1. Resolva a equações:
a) 25^x =125
b) 9^x = 243
c)(1/2)^x=(1/32)
d) (3/5)^2x=(27/125)​

Answer 1

Resposta:

Explicação passo-a-passo:

a-)

$25^x =125\\(5^2)^x=5^3\\5^{2x} =5^3\\2x=3\\x=\frac{3}{2}$

b-)

$9^x=243\\(3^2)^x=3^5\\3^{2x}=3^5\\2x=5\\x=\frac{5}{2}$

c-)

$(\frac{1}{2}) ^x=\frac{1}{32}\\(\frac{1}{2})^{x}= (\frac{1}{2})^5\\x=5$

d-)

$(\frac{3}{5})^{2x}=\frac{27}{125} \\(\frac{3}{5})^{2x}=\frac{3^3}{5^3}\\(\frac{3}{5})^{2x}=(\frac{3}{5})^3\\2x=3\\x=\frac{3}{2}$