[tex]^{3} log(12) - ^{3} log(x) = 2[/tex]
[tex] {\rm{log}_{3}12 - { \rm{log}_{3}}}x = 2[/tex]
[tex] \frac{ \rm{log}(12) }{ \rm{log}( 3)} - \frac{ { \rm{log}}(x)}{ \rm{log}(3)} = 2[/tex]
[tex] \frac{ {\rm{log}}( 12 - x)}{ \rm{log}(3)} = 2[/tex]
[tex] \frac{ {\rm{log}}( \frac{12}{x}) }{ \log (3)} = 2[/tex]
[tex] {\rm{log}(3) }\frac{{ \rm{log}}( \frac{12}{x} )}{ \rm{log}(3)} = \rm{log}(3)·2[/tex]
[tex]{ \rm{log}}( \frac{12}{x} ) = \rm{log}(3)·2[/tex]
[tex]{ \rm{log}}( \frac{12}{x} ) = 2 \: \rm{log}(3)[/tex]
[tex]{ \rm{log}}( \frac{12}{x} ) = \rm{log}( {3}^{2} )[/tex]
[tex] \frac{12}{x} = {3}^{2} [/tex]
[tex] \frac{12}{x} = 9[/tex]
[tex]x· \frac{12}{x} = x·9[/tex]
[tex]12 = x·9[/tex]
[tex]12 = 9x[/tex]
[tex] \frac{12}{9} = \frac{9x}{9} [/tex]
[tex]x = \frac{4}{3} [/tex]
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