Problem 20
Question
Write each equation in its equivalent logarithmic form. $$8^{y}=300$$
Step-by-Step Solution
Verified Answer
\(\log_{8} 300 = y\) is the logarithmic form of the given exponential equation.
1Step 1: Identify elements in the exponential equation
In the exponential equation \(8^{y}=300\), 8 is the base, y is the exponent, and 300 is the result.
2Step 2: Apply the logarithmic transformation
In the equivalent logarithmic form, the base of the exponential becomes the base of the logarithm, the result of the exponential becomes the argument of the logarithm, and the exponent of the exponential becomes the result of the logarithm. In mathematical terms, \(b^{x}=y\) translates to \(\log_{b} y = x\).
3Step 3: Write the equation in logarithmic form
Applying this logarithmic transformation gives \(\log_{8} 300 = y\). So, \(\log_{8} 300 = y\) is the equivalent logarithmic form of the original exponential equation \(8^{y}=300\).
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