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vesna_86 [32]
3 years ago
11

Evaluate log12y2, given log12y = 16. 4 32 256 65,536

Mathematics
2 answers:
Ann [662]3 years ago
8 0
32 or 256 i didn’t understand exactly what you asked
Nostrana [21]3 years ago
4 0

The value of log₁₂ y² will be : 32

Explanation


log₁₂ y²

According to the property of logarithm, if there is any exponent in the number of log, then we can just take out that exponent part to the front of the log, like: log (a)ᵇ = b × log (a)

Here, the exponent in the number of log is 2. So, according to the above property, we will get: 2 log₁₂ y

Now, the value of log₁₂ y is given as 16. So,

2 log₁₂ y

⇒ 2 (16) = 32



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The correct answers are:

_________________

 " (x − 13) ° = 53 ° " ;

_________________

 " x = 66 " ;

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 " m∠2 = 55° " ;

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 " m∠1 = 55° " .

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<u>Step-by-step explanation</u>:

Note:  The following "given values/answers" within the attached image:

Specifically:

 (x − 13)° = 72° ; and;

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   are: "incorrect"—and are "arbitrarily assigned values"

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The values and expressions given in the attached image, however, are correct/do make sense; and we can use such data to solve the problem.

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Let's start by finding the measure of ∠2 ;  that is: " m∠2 " :

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Note that:  both: "∠2 " ; and the angle that measures "175" with the attached image:

            → both form a <u>straight line</u>—that is;

              → they are "supplementary angles" ;

              → which means they add up to "180° " ;

_________________

So:  To solve for:  "m∠2" :

_________________

→  m∠2 = 180 − (125) = 55° ,

_________________

Now; to solve for:  " m∠1 " :

_________________

Note that ∠1 and ∠2 are vertical angles: which means that they have equal measurements;  

{since: vertical angles are congruent; which means that vertical angles are equal.} ;

_________________

→  As such, m∠1 = m∠2 = 55 °.

_________________

Now, take either ∠1 or ∠2 ; (each has the same "measurement"—"55° " ;

 And combine with angle with the given measurement of 72° ;

 And combine with the angle with the "given measurement of [the expression: ["x − 13"]° ;

_________________

All three of these angles form a <u>straight line</u>—that is;

              → they are "supplementary angles" ;

              → which means they add up to "180° " ;

So, 55° + 72° + (x − 13)° = 180° ;

 Let us solve for "x" ; and for "(x − 13)" ;

_________________

55 + 72 = 127 ;

→ 127 + (x − 13) = 180 ;

Now, subtract "127" from each side of the equation:

_________________

 → 127 + (x − 13) − 127 = 180 − 127 ;

   to get:

          " (x − 13) = 53 " ; →  which is one of our answers;

 Now, to solve for "x" ; we add "13" to Each Side of the equation;

   to isolate "x" on one side of the equation; & to solve for "x" :

_________________

      x − 13 + 13 = 53 + 13 ;

to get:

_________________

      x  = 66 ;

_________________

So:  The correct answers are:

_________________

 " (x − 13) ° = 53 ° " ;

  → Double check by substituting our value of "66" for "x" :

 " (66 − 13) =? 53 ?  Yes!  ;

_________________

 " x = 66 " ;

_________________

 " m∠2 = 55° " ;

_________________

 " m∠1 = 55° " .

_________________

Hope these answers—and explanations—are helpful!

  Best wishes!

_________________

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