Question

13 Determine o valor do expoente para que as sentenças se tornem verdadeiras.

a)
(3/5)? = 81/625

b)
(7/10)? = 100/49

c)
(12/17)? = 1

d)
(2/3)? = 32/248

e)
10? = 1/1000

f)
(1/8)? = 8

PRECISO URGENTE POR FAVOR!!!!!


por favor?

Answer 1

Explicação passo-a-passo:

a) $\sf \left(\dfrac{3}{5}\right)^{x}=\dfrac{81}{625}$

Veja que $\sf \left(\dfrac{3}{5}\right)^4=\dfrac{81}{625}$

$\sf \left(\dfrac{3}{5}\right)^{x}=\left(\dfrac{3}{5}\right)^4$

Assim, $\sf x=4$

b) $\sf \left(\dfrac{7}{10}\right)^{x}=\dfrac{100}{49}$

Veja que $\sf \left(\dfrac{7}{10}\right)^2=\dfrac{49}{100}$

$\sf \left(\dfrac{7}{10}\right)^{x}=\left(\dfrac{7}{10}\right)^2$

Assim, $\sf x=2$

c) $\sf \left(\dfrac{12}{17}\right)^{x}=1$

Veja que $\sf \left(\dfrac{12}{17}\right)^0=1$

$\sf \left(\dfrac{12}{17}\right)^{x}=\left(\dfrac{12}{17}\right)^0$

Assim, $\sf x=0$

d) $\sf \left(\dfrac{2}{3}\right)^{x}=\dfrac{32}{243}$

Veja que $\sf \left(\dfrac{2}{3}\right)^5=\dfrac{32}{243}$

$\sf \left(\dfrac{2}{3}\right)^{x}=\left(\dfrac{2}{3}\right)^5$

Assim, $\sf x=5$

e) $\sf 10^{x}=\dfrac{1}{1000}$

Veja que $\sf 10^{-3}=\dfrac{1}{1000}$

$\sf 10^{x}=10^{-3}$

Assim, $\sf x=-3$

f) $\sf \left(\dfrac{1}{8}\right)^{x}=8$

Veja que $\sf \left(\dfrac{1}{8}\right)^{-1}=8$

$\sf \left(\dfrac{1}{8}\right)^{x}=\left(\dfrac{1}{8}\right)^{-1}$

Assim, $\sf x=-1$