Question

Stiind ca log in baza 3 din 2=a
Demonstrati ca log in baza 16 din 24=(1+3a)/4a

Answer 1

$a = log_{3}(2)$

$log_{16}(24) = \frac{1 + 3a}{4a}$

$log_{16}(24) = \frac{ log_{3}(3) + 3 \times log_{3}(2) }{4 \times log_{3}(2) }$

$log_{ {2}^{4} }(3 \times {2}^{3} ) = \frac{ log_{3}(3) + log_{3}( {2}^{3} ) }{ log_{3}( {2}^{4} ) }$

$log_{ {2}^{4} }(3 \times {2}^{3} ) = \frac{ log_{3}(3 \times {2}^{3} ) }{ log_{3}( {2}^{4} ) }$

$log_{ {2}^{4} }(3 \times {2}^{3} ) = log_{ {2}^{4} }(3 \times {2}^{3} )$

$log_{16}(24) = log_{16}(24) \: (A)$

Formule folosite :

$1 = log_{x}(x)$

$log_{x}(y)+log_{x}(z)=log_{x}(y\:\times\:z)$

$n \times log_{x}(y) = log_{x}( {y}^{n} )$

$log_{x}(y) = \frac{ log_{z}(y) }{ log_{z}(x) }$