Question

Вычислите логарифм log5 1 log5 1/25 log5 0,04 2) log16 32 3) lo3 9 - log3 15 + log3 5

Answer 1

$log_{5}(1) = log_{5}( {5}^{0} ) = 0 \\ log_{5}( \frac{1}{25} ) = log_{5}( {5}^{ - 2} ) = - 2 \\ log_{5}(0.04) = log_{5}( \frac{4}{100} ) = \\ = log_{5}( \frac{1}{25} ) = - 2$
$log_{16}(32) = log_{ {2}^{4} }( {2}^{5} ) = \\ = \frac{5}{4} = 1.25$
$log_{3}(9) - log_{3}(15) + log_{3}(5) = \\ = log_{3}( \frac{9 \cdot 5}{15} ) = \\ = log_{3}(3) = 1$