Answer:
log₅(3125) = 5
Step-by-step explanation:
Given:
log₅(3125)
Now,
using the property of log function that
logₐ(b) = [tex]\frac{\log(b)}{\log(a)}[/tex]
thus,
Therefore, applying the above property, we get
⇒ [tex]\frac{\log(3125)}{\log(5)}[/tex] (here log = log base 10)
now,
3125 = 5⁵
thus,
⇒ [tex]\frac{\log(5^5)}{\log(5)}[/tex]
Now,
we know from the properties of log function that
log(aᵇ) = b × log(a)
therefore applying the above property we get
⇒ [tex]\frac{5\log(5)}{\log(5)}[/tex]
or
⇒ 5
Hence,
log₅(3125) = 5
