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 = log^{4}_{3} then flow that x^{b} = 64

Answer:

x^{b} = 27log^{4}_{3}

= 3^{3log43} = 3^{log(4)33}

= 3^{log643 = 64}

Question 4.

If log_{10}\(\sqrt{1+x}+3\) log_{10} \(\sqrt{1-x}\) = log_{10} \(\sqrt{1-x^{2}}+2\) . Find x.

Answer:

log_{10} (x + 1)^{1/2} + log_{10}(1 – x)^{3/2} = log_{10}(1 – x^{2})^{1/2} + log^{100}_{10}

⇒ (x + 1)^{1/2} (1 – x)^{3/2} = (1 – x^{2})^{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 log^{n}_{a} log^{n}_{6} log^{n}_{c} are in HP.

Answer:

Given, a, b, c are in GP = b^{2} = 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.