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)

log₅(3125) = 5

Step-by-step explanation:

Given:

log₅(3125)

Now,

using the property of log function that

logₐ(b) =

thus,

Therefore, applying the above property, we get

⇒   (here log = log base 10)

now,

3125 = 5⁵

thus,

⇒  

Now,

we know from the properties of log function that

log(aᵇ) = b × log(a)

therefore applying the above property we get

⇒

or

⇒ 5

Hence,

log₅(3125) = 5