Solution:Yes, our friend is correct. Explanation: 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.
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.
