   Chapter 0.8, Problem 1E

Chapter
Section
Textbook Problem

In Exercises 1–4, complete the given tables. Exponential Form 10 2 = 100 4 3 = 64 4 4 = 256 0.45 0 = 1 8 1 / 2 = 2 2 4 − 3 = 1 64 Logarithmic Form

To determine

To fill: The following table,

 Exponent Form 102=100 43=64 44=256 0.450=1 812=22 4−3=164 Logarithmic Form

Solution:

The complete table is,

 Exponent Form 102=100 43=64 44=256 0.450=1 812=22 4−3=164 Logarithmic Form log10100=2 log464=3 log4256=4 log0.451=0 log822=12 log4164=−3
Explanation

Given information:

The given table is,

 Exponent Form 102=100 43=64 44=256 0.450=1 812=22 4−3=164 Logarithmic Form

Consider the exponent, 102=100

The exponent form ac=b means logarithmic form, logab=c.

Then the exponent form 102=100 mean logarithmic form log10100=2.

Consider the exponent, 43=64

Since the exponent form ac=b means logarithmic form, logab=c.

Then the exponent form 43=64 mean logarithmic form log464=3.

Consider the exponent, 44=256

Since the exponent form ac=b means logarithmic form, logab=c.

Then the exponent form 44=256 mean logarithmic form log4256=4.

Consider the exponent, 0.450=1

Since the exponent form ac=b means logarithmic form, logab=c.

Then the exponent form 0.450=1 mean logarithmic form log0.451=0.

Consider the exponent, 812=22

Since the exponent form ac=b means logarithmic form, logab=c.

Then the exponent form 812=22 mean logarithmic form log822=12.

Consider the exponent, 43=164

Since the exponent form ac=b means logarithmic form, logab=c.

Then the exponent form 43=164 mean logarithmic form log4164=3.

Hence, the complete table is

 Exponent Form 102=100 43=64 44=256 0.450=1 812=22 4−3=164 Logarithmic Form log10100=2 log464=3 log4256=4 log0.451=0 log822=12 log4164=−3

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