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115. Simplify: \( 5^{\log _{5} 19}+\log _{7} 7^{3} \) (Section 3.2 , Example 5 )

Ask by Gibson Perkins. in the United States
Feb 04,2025

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\( 5^{\log _{5} 19} + \log _{7} 7^{3} = 22 \)

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To simplify \( 5^{\log _{5} 19}+\log _{7} 7^{3} \), start with the first term. By the property of logarithms, \( 5^{\log_{5} 19} = 19 \). For the second term, use the fact that \( \log_{7} 7^{3} = 3 \) since the logarithm of a number to its own base gives the exponent directly. Now, combine the results: \[ 5^{\log_{5} 19} + \log_{7} 7^{3} = 19 + 3 = 22. \] Thus, the simplified expression is \( 22 \).

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