Question

dados log2 = x e log 3 = y determine:
$log \: \frac{1}{3}$
$log \: 0.06$
$log \: \sqrt[3]{12}$
$log \: \sqrt{3}$

Answer 1

Log 1/3

= Log 1 - Log 3

= 0 - y

= -y

Log 0,06

= Log 6/100

= Log 6 - Log 100

= Log 2 * 3 - Log 100

= Log 2 + Log 3 - Log 100

= x + y - 2

Log ∛12

= Log 12¹/³

= 1/3 * Log 12

= 1/3 * Log 2² * 3

= 1/3 * ( 2 Log2 + Log 3 )

= 1/3 * (2 x + y)

= 2x/3 + y/3

Log √3

= Log 3¹/²

= 1/2 * Log 3

= 1/2 * y

= y/2