Odpowiedź:
1.
d)
[tex] log_{6}(10) - log_{6}( \frac{5}{18} ) + log_{6}( \sqrt{6} ) = log_{6}(10 \div \frac{5}{18} ) + \frac{1}{2} = log_{6}(36) + \frac{1}{2} = 2 + \frac{1}{2} = 2 \frac{1}{2} [/tex]
2.
b)
[tex] log_{8}(x) = \frac{ log_{5}(3) - log_{5}(75) }{ log_{2}(48) - log_{2}(6) } [/tex]
[tex] log_{8}(x) = \frac{ log_{5}( \frac{3}{75} ) }{ log_{2}(48 \div 6) } [/tex]
[tex] log_{8}(x ) = \frac{ log_{5}( \frac{1}{25} ) }{ log_{2}(8) } [/tex]
[tex] log_{8}(x) = \frac{ - 2}{3} [/tex]
[tex]x = {8}^{ - \frac{2}{3} } [/tex]
[tex]x = \frac{1}{4} [/tex]
c)
[tex] log_{0.1}(x) = \frac{ log_{3}(18) - log_{3}(2) }{ log_{3}(6) - log_{3}(18) } [/tex]
[tex] log_{0.1}(x) = \frac{ log_{3}( \frac{18}{2} ) }{ log_{3}( \frac{6}{18} ) } [/tex]
[tex] log_{0.1}(x) = \frac{ log_{3}(9) }{ log_{3}( \frac{1}{3} ) } [/tex]
[tex] log_{0.1}(x) = \frac{2}{ - 1} [/tex]
[tex]x = {0.1}^{ - 2} [/tex]
[tex]x = 100[/tex]
