Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Section 9.7 - Common Logarithms, Natural Logarithms, and Change of Base - Exercise Set - Page 586: 77

Answer

$ln 50$

Work Step by Step

$log 50$ has a base of 10, while $ln 50$ has a base of $e$. The smaller a base of a log, the greater the result. Example: $log 400$ $log 4*100$ $log 4 + log 100$ $log 4 + log 10^2$ $log 4 +2$ $2+ log 4$ $log 4 = .602$ $2+ log 4$ $2+ .602$ $2.602$ $log_2 400$ $log_2 4*100$ $log_2 4*4*25$ $log_2 4 + log_2 4 + log_2 25$ $2+2+ log_2 25$ $4+log_2 25$ $log_2 25 = 4.643856$ $4+log_2 25$ $4+4.643856$ $8.643$ In this example, the log with the smaller base ($log_2 400$) is greater than the log with the larger base ($log 400$).
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