1st PUC Basic Maths Question Bank Chapter 4 Logarithms

Students can Download Basic Maths Chapter 4 Logarithms Questions and Answers, Notes Pdf, 1st PUC Basic Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 1st PUC Basic Maths Question Bank Chapter 4 Logarithms

Logarithms

Question 1.
\(\log _{5} \frac{\sqrt[4]{25}}{625}\)
Answer:

Question 2.
Find x if log^x_0.4 = -3
Answer:

Question 3.
If x = 27, b = log⁴₃ then flow that x^b = 64
Answer:
x^b = 27log⁴₃
= 3^3log4₃ = 3^log(4)3₃
= 3^{log64₃ = 64}

Question 4.
If log₁₀\(\sqrt{1+x}+3\) log₁₀ \(\sqrt{1-x}\) = log₁₀ \(\sqrt{1-x^{2}}+2\) . Find x.
Answer:
log₁₀ (x + 1)^1/2 + log₁₀(1 – x)^3/2 = log₁₀(1 – x²)^1/2 + log¹⁰⁰₁₀
⇒ (x + 1)^1/2 (1 – x)^3/2 = (1 – x²)^1/2 – 100
⇒ \(\sqrt{1-x^{2}}\) (1 – x – 100) = 0
⇒ x = ±1. x = -99 But x ≠ ± 1, -99
∴ There is no value of x exists.

Question 5.
If x = log^a_2a, y = log^2a_3a, z = log^3a_4a. Show that xyz + 1 = 2yz.
Answer:

= 2log^2a_3a . log^3a_4a = 2yz = RHS

Question 6.
If a, b, c are GP. Prove that logⁿ_a logⁿ₆ logⁿ_c are in HP.
Answer:
Given, a, b, c are in GP = b² = ac
Taking log on both sides
2 log 6 = log a + log c
⇒ log^a_n log^b_n log^c_n are inn AP
⇒ log^a_n log^b_n log^c_n are in HP.