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Rewrite the logarithmic equation as an exponential equation.
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13. Inverse, Exponential, & Logarithmic Functions
Introduction to Logarithmic Functions
Multiple Choice
Evaluate the given logarithm.
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검증된 단계별 안내1
Recall the logarithm property that relates the logarithm of a power: \(\log_{a}(b^{c}) = c \cdot \log_{a}(b)\).
Rewrite the expression \(\log_{y}(\sqrt{y})\) by expressing the square root as an exponent: \(\sqrt{y} = y^{\frac{1}{2}}\).
Apply the logarithm power rule to get \(\log_{y}(y^{\frac{1}{2}}) = \frac{1}{2} \cdot \log_{y}(y)\).
Use the fact that \(\log_{a}(a) = 1\) for any positive base \(a \neq 1\), so \(\log_{y}(y) = 1\).
Multiply the coefficient by 1 to simplify the expression to \(\frac{1}{2} \times 1 = \frac{1}{2}\), which is the value of the logarithm.
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