What is 5log3+log4 as a single logarithm?

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Amadeu Cabanilles asked Sep 3, 2023

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What is 5log3+log4 as a single logarithm?

Mathematics
high-school

Amadeu Cabanilles asked Sep 3, 2023

by Amadeu Cabanilles

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$~~~5 \log 3 + \log4 \\\\=\log 3^5 + \log 4~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=\log(3^5 \cdot 4)~~~~~~~~~~~~~~~~~~~~~~;[\log_b(mn) = \log_b m + \log_b n]\\\\=\log(972)$

Spadel answered Sep 8, 2023

by Spadel

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