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

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In summary, to solve the given logarithm problem, one can use basic rules of logarithms and the change of base formula to rewrite the equation and solve for n. The value of n in the equation is approximately 2.077, which can be found through algebraic manipulation or using a calculator. The significance of using different bases is to simplify the logarithms and make them easier to solve. Additionally, the equation can also be solved without using logarithms by rewriting it and using basic algebra. To check if the answer is correct, one can substitute the value of n back into the original equation or use a calculator to evaluate both sides.
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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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  • #2
Try converting them to either base 10 or to the base of e.
 

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

1. How do I solve this logarithm problem?

To solve this logarithm problem, we can use the basic rules of logarithms to rewrite the equation as n^6 = log_2 (n) + log_n (486√2). Then, we can use the change of base formula to convert the logarithms to a common base, such as base 10 or base e, and solve for n.

2. What is the value of n in this equation?

The value of n in this equation is approximately 2.077. This can be found by solving the equation n^6 = log_2 (n) + log_n (486√2) using a calculator or algebraic manipulation.

3. What is the significance of using different bases in this equation?

Using different bases in this equation allows us to manipulate the logarithms and make them easier to solve. By converting the logarithms to a common base, we can use basic algebra to solve for n.

4. Can this equation be solved without using logarithms?

Yes, this equation can be solved without using logarithms. We can rewrite the equation as n^6 = n^(log_2 (1944)) = n^(log_n (486√2)) and use the fact that two exponential expressions with the same base are equal if and only if their exponents are equal. This will result in a simpler equation that can be solved using basic algebra.

5. How can I check if my answer is correct?

To check if your answer is correct, you can substitute your value of n back into the original equation and see if it satisfies the equation. You can also use a calculator to evaluate both sides of the equation separately and see if they are equal.

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