Question

O valor real de y na equação log y= log 4+ log 6 - 2log4, tudo na base 2. É:

A resposta é 3/2

Porém, preciso de ajuda com a conta. Por favor

Answer 1

$\displaystyle \log_{2}{y} =\log_{2}{4}+\log_{2}{6}-2 \log_{2}{4}$

$\displaystyle \log_{2}{y} =\log_{2}{4}+\log_{2}{6}-\log_{2}{4^2}$

$\displaystyle \log_{2}{y} =\log_{2}{4}+\log_{2}{6}-\log_{2}{16}$

$\displaystyle \log_{2}{y} =\log_{2}{\dfrac{4 \cdot 6}{16}}$

$\displaystyle \log_{2}{y} =\log_{2}{\dfrac{24}{16}}$

$\displaystyle \log_{2}{y} =\log_{2}{\dfrac{3}{2}}$

$\displaystyle y=\dfrac{3}{2}$