Answer: The correct answer is: [C]:
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" [tex]3 log_{3} 2[/tex] " .
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Step-by-step explanation:
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We are given: [tex]log _{b}x^r = r * log_{b} x[/tex] ;
We have: [tex]log_{3}8[/tex] .
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Note that the number: " 8 " ; can be written as: " 2³ " ;
→ since: " 2³ = 2 * 2 * 2 = 4 * 2 = 8 " .
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→ So: [tex]log{_{3}8 = log_{3}(2^3)[/tex] ;
→ which takes the form of the expression:
→ " [tex]log_{b}x^r[/tex] " ; in which:
" b = 3 " ;
" x = 2 " ;
" r = 3 " ;
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Now: Since: [tex]log _{b}x^r = r * log_{b} x[/tex] " ;
Substitute our known values for: " [tex]r * log_{b} x[/tex] " ; as follows"
→ " [tex]3 * log_{3} 2[/tex] " ;
→ which is:
→ Answer choice: [C]: " [tex]3 log_{3} 2[/tex] " .
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Hope this is helpful.
Best wishes to you!
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