A large open meadow near your city is shrinking in size because developers have started building new homes there.
The relationship between $A$, the area of the meadow, in hectares, and $t$, the elapsed time, in months, since the construction began is modeled by the following function.
$A=1562.5\cdot 10\^{\Large{-0.1t}}$
**How many months of construction will there be before the area of the meadow decreases to $500$ hectares?**
*Give an exact answer expressed as a base-$10$ logarithm.*
[[☃ expression 1]] months