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: " [tex]log_2}8 = ? _______________[/tex] " ; [tex]log_2}8 = ? _______________[/tex]
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Take note of the following definition of a logarithm:
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" [tex]log_{m}n = a[/tex] " ; ↔ " [tex]m^{a} =n[/tex] " ;
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in which: [tex]m[/tex] refers to the "base" ;
[tex]n[/tex] refers to the "argument" ;
[tex]a[/tex] refers to the "exponent" ;
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As such:
" [tex]log_2}8 = ? _______________[/tex] "
⇔ " [tex]2^{x} = 8[/tex] " ; 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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→ " [tex]2^{x} = 8[/tex] " ;
→ " [tex]2^{3} = 8[/tex] " ; since: " [tex]2^{3} = 2 *2 *2 = 8[/tex] " ;
→ as such: " x = 3 " ;
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Thus:
"log 2 base 8 " ;
= [tex]log{_{2}}8 = 3[/tex] .
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Hope this helps!
Best wishes to you!
