Question

Tomando log 8= 0.903.
Calcula:
a) log 64
b) log
$\sqrt[3]{800}$​

Answer 1

a)

$log(64) = log( {8}^{2} )$

Recordemos que $log ({a}^{b}) = b \times log(a)$

$2 \times log(8 )$

$2 \times 0.903$

$1.806$

b)

$log( \sqrt[3]{800} )$

$log( {800}^{ \frac{1}{3} } )$

$\frac{1}{3} \times log(800)$

$\frac{1}{3} \times log(8 \times 100)$

Recordemos que $log(a \times b) = log (a) + log (b)$

$\frac{1}{3} \times ( log(8) + log(100) )$

$\frac{1}{3} \times (0.903 + 2)$

$\frac{1}{3} \times 2.903$

$0.9676666...$