Which of the following is equivalent to log3^8?

Question

asked May 20, 2021 90.3k views

2 Answers

Ken Lyon · Answer 1 · 2021-05-24T13:24:58+0000

Answer: The correct answer is: [C]:

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"
3 log_(3) 2 " .

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Explanation:

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We are given:
log _(b)x^r = r * log_(b) x ;

We have:
log_(3)8 .

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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:
$log{_(3)8 = log_(3)(2^3)$ ;

→ which takes the form of the expression:

→ "
log_(b)x^r " ; in which:

" b = 3 " ;

" x = 2 " ;

" r = 3 " ;

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Now: Since:
log _(b)x^r = r * log_(b) x " ;

Substitute our known values for: "
r * log_(b) x " ; as follows"

→ "
3 * log_(3) 2 " ;

→ which is:

→ Answer choice: [C]: "
3 log_(3) 2 " .

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Hope this is helpful.

Best wishes to you!

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