Question

Calcule o valor de cada expressão. (logaritmo)

Answer 1

Resposta:

a)

$( log_{2}(64) + log_{6}(36) ) - log_{7}( \frac{1}{49} ) = \\ (log_{2}( {2}^{6} ) + log_{6}( {6}^{2} )) - log_{7}( {7}^{ - 2} ) = \\ (6 + 2) - ( - 2) = \\ 8 + 2 = \\ 10$

b)

$\frac{ log_{10}(1) }{ log10 } = \\ \frac{0}{1} = 0$

c)

$log_{4}( \frac{1}{256} ) - log_{ \frac{1}{16} }(2) = \\ log_{4}( {4}^{ - 4} ) - log_{ {2}^{ - 4} }(2) = \\ - 4 - ( - \frac{1}{4} ) = \\ - 4 + \frac{1}{4} = \\ - \frac{15}{4}$

d)

$( log_{0.5}( \frac{1}{32} ) + log_{3}( \sqrt{ \frac{1}{27} } ) ) .log_{ \sqrt{2} }(64) = \\ (log_{ {2}^{ - 1} }( {2}^{ - 5} ) + log_{3}( {3}^{ \frac{ - 3}{2} } )) . log_{ {2}^{ \frac{1}{2} } }( {2}^{6} ) = \\ (5 + \frac{ - 3}{2}) .12 = \\60 - \frac{36}{2} = \\ 60 - 18 = \\ 42$

e)

$\frac{ log_{4}(0.25) + 2 log_{2}( \sqrt{ 128} ) }{ log( {1000} ) ^{2} } = \\ \frac{ log_{4}( {4}^{ - 1} ) + 2 log_{2}( {2}^{ \frac{7}{2} } ) }{log_{} {( {10}^{3} )}^{2} } = \\ \frac{ - 1 + 2. \frac{7}{2} }{9} = \\ \frac{ - 1 + 7}{9} = \\ \frac{6}{9} = \frac{2}{3}$

f)

$3 log_{10}( \frac{1}{1000} ) . log_{6}(1) - {7}^{ log_{7}(6) } = \\ 3 log_{10}( {10}^{ - 3} ) .0 - {7}^{ log_{7}(6) } = \\ 0 - 6 = \\ - 6$