Question

The value of log6255 is:
o
1/5
1/4
0 1/3
0 1

Answer 1

Step-by-step explanation:

1/4 is the value of log6255

Answer 2

Complete question:

What is the value of log⁵₆₂₅

A) 1/5

B) 1/4

C) 1/3

D) 1

Answer:

The value of log⁵₆₂₅ is 1/4

Step-by-step explanation:

Given,

log⁵₆₂₅

To find,

the value of y = log⁵₆₂₅

Assumption,

Let y = log⁵₆₂₅

Concept,

Some properties of the logarithmic function:

• If b = logₐⁿ then n = aᵇ...(1)

• log(aˣ) = x log (a)......(2)

• log(ab)= log(a)+log(b)....(3)
• $\log_{a^n}^b = \frac{1}{n} \log^b_a$......(4)
• $log^a_a = 1$....(5)

Calculation,

As y = log⁵₆₂₅

$\implies y = \log^5_{5^4}$ (As 625 = 5 × 5 × 5 × 5 = 5⁴)

From property (4) we get:

⇒ y = 1/4 (log₅⁵)

From  property (5) we get:

⇒ y = 1/4 (1)

⇒ y = 1/4

Therefore, the value of log⁵₆₂₅ is 1/4.

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