Question

por favor me ajudem !!!

Answer 1

vamos lá....

a)
$\log_327=x \\ \\ 3^x=27 \\ \\ \not3^x=\not3^3 \\ \\ x=3 \\ \log_327=3$ 

b)
$\log_{ \frac{1}{5} }125=x \\ \\ ( \frac{1}{5} )^x=125 \\ \\ 5^{-x}=5^3 \\ \\ -x=3~~\times(-1) \\ \\ x=-3$ 

c)
$\log_4 \sqrt{32} =x \\ \\ 4^x= \sqrt{32} \\ \\ 4^x= \sqrt{2^5} \\ \\ 2^{2x} =2^{ \frac{5}{2} } \\ \\ 2x= \frac{5}{2} \\ \\ 4x=5 \\ \\ x= \frac{5}{4}$

d)
$\log_{ \frac{2}{3} } \frac{8}{27} =x \\ \\ ( \frac{2}{3} )^x= \frac{8}{27} \\ \\ ( \frac{2}{3} )^x= \frac{2^3}{3^3} \\ \\ ( \frac{2}{3}) ^x=( \frac{2}{3} )^x \\ \\ x=3$