Question

5log to the base5 625​

Answer 1

Step-by-step explanation:

Let me help you with this problem.

We have to evaluate log 4√25/625 to the base 5.

i-e,  log₅ 4 √ (25/625) = ?

Solution:

   log₅ 4√ (25/625)

=  log₅ 4√ (1 / 25)

= log₅ 4√ (1 / 5²)

= log₅ √ [√ (1 / 5²)]    [ ∵  ⁴√ a = √ (√a) ]

Now we use the base formula which states that if a and b are greater then zero and also not equal to 1 then,

log ₐ (x) = log b (x) / log b (a)

Thus we get,

[log √ (1/5) ] /  [log (1/5) ]

which is the exact form of the given equation.

The decimal form of the given equation is

log (0.089) / log (0.2)

= - 0.21 / -0.14

= 1.5 

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