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

Answer:

log₅(3125) = 5

Step-by-step explanation:

Given:

log₅(3125)

Now,

using the property of log function that

logₐ(b) = $\frac{\log(b)}{\log(a)}$

thus,

Therefore, applying the above property, we get

⇒ $\frac{\log(3125)}{\log(5)}$   (here log = log base 10)

now,

3125 = 5⁵

thus,

⇒  $\frac{\log(5^5)}{\log(5)}$

Now,

we know from the properties of log function that

log(aᵇ) = b × log(a)

therefore applying the above property we get

⇒ $\frac{5\log(5)}{\log(5)}$

or

⇒ 5

Hence,

log₅(3125) = 5