Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 7 Exponential and Logarithmic Functions - 7.5 Apply Properties of Logarithms - 7.5 Exercises - Skill Practice - Page 510: 42



Work Step by Step

We know that $x\log_ab=\log_ab^x$, $\log_ab+\log_ac=\log_a(bc)$ and that $\log_ab-\log_ac=\log_a(b/c)$ Hence here $2(\log_320-\log_34)+0.5\log_34=2\log_320-2\log_34+\log_34^{0.5}=\log_320^2-\log_34^2+\log_32=\log_3400-\log_316+\log_32=\log_3(400/16\cdot2)=\log_350$
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