Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.12

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Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.12

Question 1.
Let b > 0 and b ≠ 1. Express y = b^x in logarithmic form. Also state the domain and range of the logarithmic function.
Solution:
Given y = b^x ⇒ log_by = x, x ∈ R with range (0, ∞) (-∞, ∞)

Question 2.
Compute log₉27 – log₂₇9.
Solution:
Let log₉27 = x ⇒ 27 = 9^x ⇒ 3³ = (3²)^x = 3^2x
⇒ 2x = 3 ⇒ x = 3/2
Let log₂₇9 = x

Question 3.
Solve log₈x + log₄x + log₂x = 11
Solution:

Question 4.

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Question 5.

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Question 6.

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Another methods

Question 7.

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Question 8.

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Question 9.

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Question 10.

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Question 11.

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Question 12.
Solve log_{5 – x}(x² – 6x + 65) = 2
Solution:
log_{5 – x}(x² – 6x + 65) = 2
⇒ x² – 6x + 65 = (5 – x)²
x² – 6x + 65 = 25 + x² – 10x
⇒ x² – 6x + 65 – 25 – x² + 10x = 0
4x + 40 = 0 ⇒ 4x = -40
x = -10

Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.12 Additional Questions

Question 1.

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Question 2.

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Question 3.

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Question 4.

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