Question

Calcule o valor de x:
a) logx 8 = 3
b) logx
$\frac{1}{16}$
=2
c) log2 x=5
d) log9 27 = x
e) log
$\frac{1}{2}$
32 = x
​

Answer 1

a) logx 8 = 3               b) logx  1/16= 2

     $x^{3} = 8\\x = 2^{3}\\x = 2$                         $x^{2} = \frac{1}{16}\\\\ x^{2} = \frac{1}{4^{2} } \\x = \sqrt[2]{\frac{1}{4^{2} } } \\x = \frac{1}{4}$

c) log2 x=5                     d) log9 27 = x               e) log

1/2 32 = x

 $2^{5} = x\\32 = x$                             $9^{x} = 27\\3^{2^{(x)} } = 27\\3^{2^{(x)} } = 3^{3} \\2 x = 3\\x = 3/2$                    $(\frac{1}{2})^{x} = 32\\ (\frac{1}{2})^{x} = 2^{5} \\x = 5$