Chapter 7 - Exponential and Logarithmic Functions - 7-3 Logarithmic Functions as Inverses - Practice and Problem-Solving Exercises - Page 458: 80

$4$

Recall (1) $\log_a{b}=y \longleftrightarrow a^y=b$ (2) The value of the function $f(x)=\log_a{x}$ increases as $x$ increases. Let $y=\log_3{38}$ Use the definition in (1) above to obtain: $3^y=38$ Note that $3^3=27$ while $3^4=81$ Since $27\lt 38 \lt 81$, then $y$ must be between $3$ and $4$. Thus, the least integer that is greater than $\log_3{38}$ is $4$.