Solve Log Problem: n^6 = log_2n(1944) = log_n(486√2)

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SUMMARY

The discussion centers on solving the equation log2n(1944) = logn(486√2) to evaluate n6. Participants highlight the importance of converting logarithmic bases, suggesting the use of base 10 or natural logarithms (base e) for simplification. The key takeaway is that transforming the logarithmic expressions correctly is essential for finding the value of n and subsequently n6.

PREREQUISITES
  • Understanding of logarithmic properties and conversions
  • Familiarity with logarithmic equations and their solutions
  • Knowledge of base conversions, specifically to base 10 and natural logarithms
  • Basic algebra skills for manipulating equations
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  • Learn how to convert logarithmic bases using the change of base formula
  • Explore properties of logarithms, including product, quotient, and power rules
  • Study examples of solving logarithmic equations in various bases
  • Practice evaluating exponential expressions derived from logarithmic equations
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Students tackling logarithmic equations, educators teaching logarithmic properties, and anyone preparing for algebra or calculus examinations.

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Homework Statement


If log[tex]_{}2n[/tex](1944) = log[tex]_{}n[/tex](486[tex]\sqrt{}2[/tex]) then evaluate n^6

P.S the 2n and n are subscripts.

Homework Equations



log base b(a) = c is the same as a^c = b

The Attempt at a Solution



I tried converting log base 2n to log base n but I ended up nowhere.
 
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Try converting them to either base 10 or to the base of e.
 

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