Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 351: 1

Answer

$"...x..."$ $log{10^3}=3$ $log{10^2}=2$ $log{10^1}=1$ $log{10^0}=0$ $log{10^{-1}}=-1$ $log{10^{-2}}=-2$ $log{10^{-3}}=-3$ $log{10^\frac{1}{2}}=\frac{1}{2}$

Work Step by Step

According to the definition of $logarithms$, it is a value in which we have to raise the $base$ to get $x$. To fill the table, we can simply input $x$ value into $log{x}$: (Note. If the $argument$ is equal to the $base$ then the answer for expression is exponent value of the $argument$ itself) $x=10^3$; $log{10^3}=3$ $x=10^2$; $log{10^2}=2$ $x=10^1$; $log{10^1}=1$ $x=10^0$; $log{10^0}=0$ $x=10^{-1}$; $log{10^{-1}}=-1$ $x=10^{-2}$; $log{10^{-2}}=-2$ $x=10^{-3}$; $log{10^{-3}}=-3$ $x=10^{\frac{1}{2}}$; $log{10^\frac{1}{2}}=\frac{1}{2}$ Also note that if the $base$ is omitted it means that the $base$ is $10$.
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