## Algebra 2 Common Core

$3$
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 $y=\log_{1.5}{2.5}$ Use the definition in (1) above to obtain: $1.5^y=2.5$ Note that $1.5^2=2.25$ while $1.5^3=3.375$ Since $2.25\lt 2.5 \lt 3.375$, then $y$ must be between $2$ and $3$. Thus, the least integer that is greater than $\log_{1.5}{2.5}$ is $3$.