Question

Logaritmos : Calcule os valores de x:
A)log2/3 8/27= x
B) logx 1/16= 2
C) log2 x = 5
D)log9 27 = x

Answer 1

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

b)
$log_{x} \frac{1}{16}= 2\\ x^2= \frac{1}{16} \\ x^2= \sqrt{ \frac{1}{16}} \\ x= \frac{1}{4}$

c) 
$log_{2} x= 5\\ 2^5= x \\ 32=x \\ x=32$

d) $log_{9} 27=x \\ 9^x=27 \\ (3^x)^2= 3^3 \\ 3^{2x}= 3^3 \\ 2x=3 \\ x= \frac{3}{2}$