Question
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Answer
\( n = 6 \)
Solution
Given that \( V_{2}{ }^{n}=64 \), we need to find the value of ' \( n \)'.
To solve this, we can use the property of exponents that states \( a^{b} = c \) implies \( b = \log_{a}(c) \).
In this case, we have \( 2^{n} = 64 \), so we can take the logarithm base 2 of both sides to solve for ' \( n \)'.
Let's calculate the value of ' \( n \)'.
Solve the equation by following steps:
- step0: Solve for \(n\):
\(2^{n}=64\)
- step1: Rewrite in exponential form:
\(2^{n}=2^{6}\)
- step2: Set the exponents equal:
\(n=6\)
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Simplify this solution Extra Insights
To solve for \( n \), you can convert 64 into a power of 2. Since \( 2^6 = 64 \), we rewrite the equation as \( V_{2}{ }^{n} = 2^6 \). Now, since the bases are the same (2), we can set the exponents equal to each other: \( n = 6 \). Another way to think about this is through the concept of logarithms! If you're comfortable with them, you could say \( n = \log_{2}{64} \). This approach succinctly gives you \( n = 6 \), reinforcing your understanding of the relationship between exponentiation and logarithmic functions. Don't forget to practice with more examples for mastery!
