Question
Write the equation in its equivalent logarithmic form. \( 66^{4}=1296 \)
Ask by Young Reeves. in Saudi Arabia
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The logarithmic form of the equation \( 66^{4} = 1296 \) is \( \log_{66}(1296) = 4 \).
Solution
To convert the equation \( 66^{4} = 1296 \) into its equivalent logarithmic form, we follow these steps:
1. Identify the base, which is \( 66 \).
2. Identify the exponent, which is \( 4 \).
3. Identify the result, which is \( 1296 \).
The logarithmic form of the equation can be expressed as:
\[
\log_{b}(a) = c
\]
where \( b \) is the base, \( a \) is the result, and \( c \) is the exponent.
Thus, the equivalent logarithmic form of the equation \( 66^{4} = 1296 \) is:
\[
\log_{66}(1296) = 4
\]
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Simplify this solution Beyond the Answer
To express the equation \( 66^{4} = 1296 \) in logarithmic form, we can rewrite it as \( \log_{66}(1296) = 4 \). This means that the base \( 66 \) raised to the power of \( 4 \) results in \( 1296 \). Logarithms are like the superhero sidekicks of exponents, translating the powers we raise numbers to into more manageable forms! When tackling logarithmic equations, remember to keep the base consistent. A common mistake is to change the base incorrectly, leading to confusion. Always double-check your bases and ensure they're in line with the original exponential equation for accurate conversions!
