Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 406: 103

For $9^x=20$: $1\lt x \lt2$ For $9^x=100$: $2\lt x \lt3$

We look at powers of $9$: $9^{1}=9$ $9^{2}=81$ $9^{3}=729$ We know that the solution to $9^{x}=20$ must have an $x$ value between $1$ and $2$ because $20$ is between $9$ and $81$. We also know that the solution to $9^x=100$ must have an $x$ value between $2$ and $3$ because $100$ is between $81$ and $729$.