Question

Evaluate log 2 base 8​

Answer 1

Answer: The correct answer is: " 3 " .

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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!