Question

Sendo log10 2=0,3 e log10 3=0,5, calcule log3 12

Answer 1

Explicação passo-a-passo:

$\sf log_{3}~12$

$\sf =\dfrac{log_{10}~12}{log_{10}~3}$

$\sf =\dfrac{log_{10}~(2^2\cdot3)}{log_{10}~3}$

$\sf =\dfrac{log_{10}~2^2+log_{10}~3}{log_{10}~3}$

$\sf =\dfrac{2\cdot log_{10}~2+log_{10}~3}{log_{10}~3}$

$\sf =\dfrac{2\cdot0,3+0,5}{0,5}$

$\sf =\dfrac{0,6+0,5}{0,5}$

$\sf =\dfrac{1,1}{0,5}$

$\sf =\dfrac{11}{5}$

$\sf =2,2$