5log to the base5 625
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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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