Question

Evaluate each of the following in terms of x and y, if it is given x=log, 3 and
y=log 5 base2
(i) log15base2
(ii) log 7.5base2 (iii) log60base2 (iv) log6750bsae2
please answer fast​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

(i) log₂15 = x + y

(ii) log₂(7.5) = x + y - 1

(iii) log₂60 = x + y + 2

(iv) log₂(6750) = 3x + 3y + 1

Step-by-step explanation:

Given: x = log₂3 and y = log₂5

(i) Given: log₂15

= log₂(3×5)

= log₂3 + log₂5

= x + y

So, log₂15 = x + y

(ii) Given: log₂(7.5)

= log₂ (15/2)

= log₂ 15 - log2

= log₂(3×5) - 1

= log₂3 + log₂5 - 1

= x + y - 1

So, log₂(7.5) = x + y - 1

(iii) Given: log₂60

= log₂ (15×4)

= log₂15 + log₂4

= log₂ (3×5) + log₂ (2²)

= log₂3 + log₂5 + 2 log₂2

= x + y + 2

So, log₂60 = x + y + 2

(iv) Given: log₂ 6750

= log₂ (15×45×10)

= log₂ (3×5×3×3×5×2×5)

= log₂ (3³ × 5³ × 2)

= log₂3³ + log₂5³ + log₂2

= 3 log₂3 + 3 log₂5 + 1

= 3x + 3y + 1

So, log₂(6750) = 3x + 3y + 1

Formulas used :-

1) logₐ (mn) = logₐm + logₐn

2) logₐ (m/n) = logₐm - logₐn

3) logₐ (mⁿ) = n logₐm

4) logₐ a = 1