Question

What is the value of log381?

Answer 1

log 381 = ln 381.

ln 381 = ln 3 + ln 127

Answer: 5.9427993751

Answer 2

Answer: The correct answer is: " 4 " .

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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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