Question

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)

Answer 1

log₅(3125) = 5

Explanation:

Given:

log₅(3125)

Now,

using the property of log function that

logₐ(b) =
`(\log(b))/(\log(a))`

thus,

Therefore, applying the above property, we get

⇒
`(\log(3125))/(\log(5))` (here log = log base 10)

now,

3125 = 5⁵

thus,

⇒
`(\log(5^5))/(\log(5))`

Now,

we know from the properties of log function that

log(aᵇ) = b × log(a)

therefore applying the above property we get

⇒
`(5\log(5))/(\log(5))`

or

⇒ 5

Hence,

log₅(3125) = 5