Exercise 58 Page 304

Start by simplifying the exponential expression.

Yes, see solution.

Practice makes perfect

We are given ( 1a)^x=b. We know that a>1 and b>1, but we need to determine the values of x that satisfy these conditions. Let's start by simplifying the equation.

(1/a)^x=b

PowQuot

(a/b)^m=a^m/b^m

1^x/a^x=b

ExponentOne

a^1=a

1/a^x=b

To make this easier to comprehend, let's substitute a value for a. We will use 2. 1/2^x=b Notice that if we substitute any non-negative x-value into this equation, b will not be greater than one.

x	b
0	1/2^0=1/1=1
1	1/2^1=1/2
2	1/2^2=1/4
3	1/2^3=1/8

This will continue as our x-values get larger and for any a-value greater than 1. Since no positive value of x will satisfy b>1, the value of x must be negative to satisfy the equation. Therefore, our friend is correct.

Subchapter links

Communicate Your Answer p.299

Monitoring Progress p.300-302

Exercises p.303-304

Exercise 58 Page 304

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