Question

Evaluate log 2 base 8​

Answer 1

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:  " $log_2}8 = ? _______________$  " ;  $log_2}8 = ? _______________$

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Take note of the following definition of a logarithm:

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"   $log_{m}n = a$ " ;  ↔  " $m^{a} =n$  "  ;

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in which:  $m$  refers to the "base" ;

               $n$  refers to the "argument" ;

               $a$  refers to the "exponent" ;

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As such:

       " $log_2}8 = ? _______________$ "

      ⇔ " $2^{x} = 8$ " ; 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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 → " $2^{x} = 8$ " ;

 → " $2^{3} = 8$ " ;  since: " $2^{3} = 2 *2 *2 = 8$ " ;

 → as such:   " x = 3  " ;

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Thus:

"log 2 base 8 " ;

          = $log{_{2}}8 = 3$  .

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Hope this helps!

Best wishes to you!