Question

What is the value of log381?

Answer 1

Answer:  The correct answer is:   " 4 " .

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Step-by-step explanation:

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We are given:  

"  log₃ 81 "  ;  

Note:  "   logₐ xⁿ  =  n logₐ x " ;  

So:  a = 3 ;  

xⁿ  = ? ;  ↔  $3^{y} = 81 ;$

Solve for "y" ;

3² = 3 * 3 = 9 ;

3³ = 3 * 3 * 3 = (3 * 3) * 3 = 9 * 3 = 27 ;

3⁴ = 3 * 3 * 3 * 3 = (3 * 3) * 3 * 3 =  9 * 3 * 3 = (9 * 3) * 3 = 27 * 3 = 81 ;

  →  3⁴  = 81 .

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"  log₃ 81 "  ;  

Note:  "   logₐ xⁿ  =  n logₐ x " ;  

So:  a = 3 ;  x = 3 ;  and n = 4 ;  

Since:  Given:  " log₃ 81 "  ;  

    →    log₃ 81 ;  ↔  81 = xⁿ = 3⁴ ;

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    →     log₃ 81 =  log₃ 3⁴ ;  =  n logₐ x ;  

    →    n logₐ x   =  ?   ; Substitute:  "a = 3 " ;  "x = 3" ; "n = 4" ;

    →    4 log₃ 3  =  ? ;

                         =   4 * log₃ 3  ;

     →  log₃ 3 = ?   ;  →$3^{?} = 3$  ;  ↔  3¹ = 3 ;

                                                                    ↔  log₃ 3 = 1 .

     →  4 * log₃ 3  =  4 * 1  =  4.

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    The answer is:  " 4 " .

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Answer 2

log 381 = ln 381.

ln 381 = ln 3 + ln 127

Answer: 5.9427993751