Consider the logarithms base 5. For each logarithmic expression below, either calculate the value of the expression or explain why the expression does not make sense.log5(3125)

Accepted Solution

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