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Answer: The correct answer is: " 3 " .
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Step-by-step explanation:
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The problem given is:
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Evaluate: log 2 base 8 .
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Rewrite as: " " ;
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Take note of the following definition of a logarithm:
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" " ; ↔ "
" ;
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in which: refers to the "base" ;
refers to the "argument" ;
refers to the "exponent" ;
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As such:
" "
⇔ " " ; Solve for "x" ;
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Note:
2⁰ = 1 ;
2¹ = 2 ;
2² = 2 * 2 = 4 ;
2³ = 2 * 2 * 2 = 8 .
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→ " " ;
→ " " ; since: "
" ;
→ as such: " x = 3 " ;
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Thus:
"log 2 base 8 " ;
= .
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Hope this helps!
Best wishes to you!