Question
4) Use properties of logarithms to evaluate the expression. Assume all expressions exist and are well-defined. \( \log _{w} w^{11}-\log _{w} w^{2} \)
Ask by Reese Chambers. in the United States
Mar 14,2025
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The expression \( \log_{w} w^{11} - \log_{w} w^{2} \) simplifies to 9.
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To evaluate \( \log_{w} w^{11} - \log_{w} w^{2} \), we can apply the properties of logarithms. The first logarithm simplifies to the exponent due to the identity \( \log_{b} b^{x} = x \). Therefore, \( \log_{w} w^{11} = 11 \) and \( \log_{w} w^{2} = 2 \). Putting it all together, we have: \[ 11 - 2 = 9 \] So, the expression evaluates to \( 9 \).