Question

Por favor me ajudem!
$a) \: \: E = \frac{1}{2} \times log_{6}256 + 3 \times log_{6}9 + 2 \times log_{6}12$
$b) \: E = log_{9}125 \times log_{8}7 \times log_{5}64 \times log_{49}81$

​

Answer 1

Explicação passo-a-passo:

a)

$E = \frac{1}{2} \times log_{6}256 + 3 \times log_{6}9 + 2 \times log_{6}12$

$E = log_{6}(256 {}^{ \frac{1}{2} } ) + log_{6}( {9}^{3} ) + log_{6}(12 {}^{2} )$

$E = log_{6}(256 {}^{ \frac{1}{2} } \times {9}^{3} \times {12}^{2} )$

$E = log_{6}(144 \times 256 {}^{ \frac{1}{2} } \times 729 )$

$E = log_{6}(104976 \times 256 {}^{ \frac{1}{2} } )$

$E = log_{6}(104976 \times (2 {}^{8} ) {}^{ \frac{1}{2} } )$

$E = log_{6}(104976 \times 2 {}^{4} )$

$E = log_{6}(104976 \times 16)$

$E = log_{6}(1679616)$

$E = log_{6}(6 {}^{8} )$

$E = 8$

b)

$E = log_{9}125 \times log_{8}7 \times log_{5}64 \times log_{49}81$

$E = log_{3 {}^{2} }(5 {}^{3} ) log_{2 {}^{3} }(7) log_{5}(2 {}^{6} ) log_{7 {}^{2} }(3 {}^{4} )$

$E = \frac{3}{2} \times log_{3}(5) \frac{1}{3} \times log_{2}(7) 6 log_{5}(2) log_{7}(3)$

$E = log_{3}(5) log_{2}(7) \times 6 log_{5}(2) log_{7}( 3)$

$E = \frac{ log_{7}(5) }{ log_{7}(3) } \times log_{2}(7) \times 6 log_{5}(2) log_{7}(3)$

$E = log_{7}(5) log_{2}(7) \times 6 log_{5}(2)$

$E = \frac{ log_{2}(5) }{ log_{2}(7) } \times log_{2}(7) \times 6 log_{5}(2)$

$E = log_{2}(5) \times 6 log_{5}(2)$

$E = 1 \times 6$

$E = 6$

Espero te ajudado !!!