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Type the correct answer in the box. Use numerals instead of words. What is the value of this expression? \log _{2}\,8\: \:\log _{3}\left ( \frac{1}{3} \right )\:=

Sagot :

regalmocha17

Answer:

-3

Step-by-step explanation:

Given the expression:

[tex]\log_{2} 8 \times \log_{3}(\frac{1}{3})[/tex]

Determine the value.

[tex]\log_{2} 8 = 3[/tex]

Log base 2 of 8 is 3 because we're simply trying to determine to what power does 2 equal 8. In this case, it would be 3.

[tex]\log_{3}(\frac{1}{3}) = -1 \\[/tex]

Same thing here, to what power does 3 equal to 1/3? That would be -1.

Now, multiply both sides together to get the final value (product).

[tex]3 \times -1 = -3[/tex]

Therefore, the value of the expression of log base 2 of 8 multiplied by log base 3 of 1/3 would be equal to -3.

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