Question

se log23=k entao log49 é:

a)2k
b)k2
c)k
d)k3
e)k/2

Answer 1

Resposta:

$log_{2}(3) = k \\ \\ {2}^{k} = 3 \\ \\ log_{4}(9) = x \\ \\ {( {2}^{2} )}^{x} = 9 \\ \\ {2}^{2x} = {3}^{3} \\ \\ log_{2}( {2}^{2x} ) = log_{2}( {3}^{3} ) \\ \\ 2x \times log_{2}(2) = 3 \times log_{2}(3) \\ \\ 2x \times 1 = 3 \times k \\ \\ 2x = 3k \\ \\ \blue{x = \dfrac{3k}{2} }$