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Without using a calculator, find the value of the following logarithmic expression. \( \log _{2} 32 \)

Ask by Perkins Rose. in Switzerland
Nov 19,2024

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\( \log_{2}(32) \)

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To find the value of \( \log_{2} 32 \), we need to express 32 as a power of 2. Recognizing that \( 32 = 2^5 \), we can rewrite the logarithm: \[ \log_{2} 32 = \log_{2} (2^5) \] By using the property of logarithms that states \( \log_{b} (b^x) = x \), we can simplify this expression: \[ \log_{2} (2^5) = 5 \] Thus, the value of \( \log_{2} 32 \) is \( 5 \).

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